What do the grand tournament accommodations options do in CK3?

Ramshackle Tents: Certain negative events are more likely to fire. Simple Pavilions: Event weightings are unaffected. Luxurious Encampments: Certain negative events are less likely to fire.

What do the grand tournament prizes options do in CK3?

Simple Prizes: Prize Artifacts will be of Common Rarity. Decent Prizes: Prize Artifacts will be of Common or Masterwork Rarity. Fine Prizes: Prize Artifacts will be of Masterwork or Famed Rarity. Good Prizes: Prize Artifacts will be of Masterwork, Famed, or Illustrious Rarity. Splendid Prizes: Prize Artifacts will be of Famed or Illustrious Rarity.

How long is the grand tournament cooldown?

10 years: the base its cooldown value starts from (patch 1.20.0.3).

Activity

Grand Tournament

Tours and Tournaments

Grand Tournament is an activity in Crusader Kings III for up to 250 guests. Its options: accommodations (Ramshackle Tents, Simple Pavilions and Luxurious Encampments) and prizes (Simple Prizes, Decent Prizes, Fine Prizes, Good Prizes and Splendid Prizes). Host intents: Recreation, Triumph, Recruit, Murder, Seduce and 2 more. Cooldown 10 years at base. Its cost script uses gold and treasury. It needs Tours and Tournaments. Patch 1.20.0.3, from game/common/activities/activity_types/tournament.txt.

Quick answers (3)

What do the grand tournament accommodations options do in CK3?: Ramshackle Tents: Certain negative events are more likely to fire. Simple Pavilions: Event weightings are unaffected. Luxurious Encampments: Certain negative events are less likely to fire.
What do the grand tournament prizes options do in CK3?: Simple Prizes: Prize Artifacts will be of Common Rarity. Decent Prizes: Prize Artifacts will be of Common or Masterwork Rarity. Fine Prizes: Prize Artifacts will be of Masterwork or Famed Rarity. Good Prizes: Prize Artifacts will be of Masterwork, Famed, or Illustrious Rarity. Splendid Prizes: Prize Artifacts will be of Famed or Illustrious Rarity.
How long is the grand tournament cooldown?: 10 years: the base its cooldown value starts from (patch 1.20.0.3).

Host a magnificent set of martial or cultural Contests, attracting contenders from near and far to compete in hastiludes for Prizes and Prestige.

Accommodations

Ramshackle Tents
- Certain negative events are more likely to fire
What matters more, the skills on display or the place you display them?
Adds to the cost: gold / treasury
Simple Pavilions
- Event weightings are unaffected
The key to a decent bout is getting a good night's rest.
Adds to the cost: gold / treasury
Luxurious Encampments
- Certain negative events are less likely to fire
Tournaments should be more than just sporting events, they should be entire sporting experiences.
Adds to the cost: gold / treasury

Prizes

Simple Prizes
- Prize Artifacts will be of Common Rarity
We're here for the love of sport, the baubles on offer are just an excuse.
Adds to the cost: gold / treasury
Decent Prizes
- Prize Artifacts will be of Common or Masterwork Rarity
While we're not here for the prizes, being able to fund the journey home is a very practical goal.
Adds to the cost: gold / treasury
Fine Prizes
- Prize Artifacts will be of Masterwork or Famed Rarity
Without stakes, what's the point in a competition?
Adds to the cost: gold / treasury
Good Prizes
- Prize Artifacts will be of Masterwork, Famed, or Illustrious Rarity
A prize isn't just a bauble handed out to the victor, it is a beacon for attracting the brave and bold to attend.
Adds to the cost: gold / treasury
Splendid Prizes
- Prize Artifacts will be of Famed or Illustrious Rarity
The best prizes are the ones so glamorous that they eclipse their winners.
Adds to the cost: gold / treasury

Host intents

RecreationYou want to focus on reducing stress by looking for Stress-relieving opportunities.
TriumphWin contests at this Activity Tournament, at the cost of all else. This often leads to increased Progress to Victory rewards and special options and events.
RecruitYou seek to improve your court with new and powerful Knights. This often leads to recruiting opportunities.
MurderYou're focused on ending the life of your target. This often results in murder occasions and special options.
SeduceYou have one and only one thing in mind: seducing your target. This often leads to special events and options to fullfil that desire.
BefriendYou are set to gain your target's favor. This often leads to friendly events and options.
Evangelize TenetYou want to preach your Personal Tenet to receptive guests, that they may adopt it as their own, increasing Tenet Popularity.

Guest intents

RecreationYou want to focus on reducing stress by looking for Stress-relieving opportunities.
TriumphWin contests at this Activity Tournament, at the cost of all else. This often leads to increased Progress to Victory rewards and special options and events.
RecruitYou seek to improve your court with new and powerful Knights. This often leads to recruiting opportunities.
MurderYou're focused on ending the life of your target. This often results in murder occasions and special options.
SeduceYou have one and only one thing in mind: seducing your target. This often leads to special events and options to fullfil that desire.
BefriendYou are set to gain your target's favor. This often leads to friendly events and options.
Evangelize TenetYou want to preach your Personal Tenet to receptive guests, that they may adopt it as their own, increasing Tenet Popularity.

Phases

MeleeA mock battle, on horse and on foot, between two teams vying to control a contested field and capture opposing combatants for ransom. Contest Format: Teams
ArcheryA bow competition in which each contestant shoots at a target with a set number of arrows, aiming to score as many points as possible. Contest Format: Turns
RecitalA poetry competition in which each contestant publicly recites a poem written for the occasion, and is judged against all other entrants. Contest Format: Turns
JoustAn equestrian competition in which contestants tilt with lances, attempting to unhorse or score more points than their foes to be the last standing. Contest Format: Knock-Out Number of Contest Rounds: 3
WrestlingA contest of strength and cunning, in which contestants attempt to knock down or throw their foes from the ring to be the last standing. Contest Format: Knock-Out Number of Contest Rounds: 3
DuelA series of armed duels fought on foot, in which contestants attempt to disarm or score more points than their foes to be the last standing. Contest Format: Knock-Out Number of Contest Rounds: 3
Board GameA contest of wits in which contestants play a series of board game matches, with the ultimate winner being the last remaining player. Contest Format: Knock-Out Number of Contest Rounds: 3
Horse RaceA spectator sport in which lords and ladies enter horses to race against each other, with the winner being the first to cross the finishing line. Contest Format: Race
CeremonyThe closing ceremony and celebrations!

Who can host it (is_shown) (6 lines of game script)

highest_held_title_tier > tier_barony
is_landed = yes
has_dlc_feature = tours_and_tournaments
has_dlc_feature = advanced_activities
ai_activity_war_check = yes
ai_activity_coronation_check = yes

As written in game/common/activities/activity_types/tournament.txt.

Cost (205 lines of game script)

gold = {
	value = 0
	if = {
		limit = {
			OR = {
				has_treasury = no
				government_has_flag = government_is_theocracy
			}
		}
		add = {
			add = {
				value = tournament_base_cost
				desc = tournament_base_cost
			}
			add = {
				value = tournament_base_cost
				multiply = activity_cost_scale_by_era
				subtract = tournament_base_cost
				desc = activity_cost_scale_by_era_desc
			}
			if = {
				limit = {
					scope:province ?= {
						has_building_or_higher = hall_of_heroes_01
					}
				}
				add = {
					value = 0
					add = {
						value = tournament_base_cost
						add = {
							value = tournament_base_cost
							multiply = activity_cost_scale_by_era
							subtract = tournament_base_cost
						}
					}
					multiply = tournament_activity_cost_max_discount_value
					desc = tournament_activity_cost_max_discount_desc
				}
			}
			if = {
				limit = {
					scope:province ?= {
						has_building_or_higher = war_camps_01
					}
				}
				add = {
					value = 0
					add = {
						value = tournament_base_cost
						add = {
							value = tournament_base_cost
							multiply = activity_cost_scale_by_era
							subtract = tournament_base_cost
						}
					}
					multiply = tournament_activity_cost_discount_value
					desc = tournament_activity_cost_discount_war_camps_desc
				}
			}
			if = {
				limit = {
					scope:province ?= {
						has_building_or_higher = barracks_01
					}
				}
				add = {
					value = 0
					add = {
						value = tournament_base_cost
						add = {
							value = tournament_base_cost
							multiply = activity_cost_scale_by_era
							subtract = tournament_base_cost
						}
					}
					multiply = tournament_activity_cost_discount_value
					desc = tournament_activity_cost_discount_barracks_desc
				}
			}
			if = {
				limit = {
					factor_zero_if_entitled_to_freebie_activity_trigger = yes
				}
				multiply = 0
			}
			min = 0
			if = {
				limit = {
					is_ai = yes
					has_character_flag = tournament_ai_override
				}
				multiply = 0
			}
		}
	}
	if = {
		limit = {
			confederation ?= {
				has_cohesion_level_parameter = any_member_activity_cost_reduced
			}
		}
		multiply = {
			value = 0.9
			desc = CB_COHESION_PARAMETER_DISCOUNT
		}
	}
}
treasury = {
	value = 0
	if = {
		limit = {
			has_treasury = yes
			NOT = {
				government_has_flag = government_is_theocracy
			}
		}
		add = {
			add = {
				value = tournament_base_cost
				desc = tournament_base_cost
			}
			add = {
				value = tournament_base_cost
				multiply = activity_cost_scale_by_era
				subtract = tournament_base_cost
				desc = activity_cost_scale_by_era_desc
			}
			if = {
				limit = {
					scope:province ?= {
						has_building_or_higher = hall_of_heroes_01
					}
				}
				add = {
					value = 0
					add = {
						value = tournament_base_cost
						add = {
							value = tournament_base_cost
							multiply = activity_cost_scale_by_era
							subtract = tournament_base_cost
						}
					}
					multiply = tournament_activity_cost_max_discount_value
					desc = tournament_activity_cost_max_discount_desc
				}
			}
			if = {
				limit = {
					scope:province ?= {
						has_building_or_higher = war_camps_01
					}
				}
				add = {
					value = 0
					add = {
						value = tournament_base_cost
						add = {
							value = tournament_base_cost
							multiply = activity_cost_scale_by_era
							subtract = tournament_base_cost
						}
					}
					multiply = tournament_activity_cost_discount_value
					desc = tournament_activity_cost_discount_war_camps_desc
				}
			}
			if = {
				limit = {
					scope:province ?= {
						has_building_or_higher = barracks_01
					}
				}
				add = {
					value = 0
					add = {
						value = tournament_base_cost
						add = {
							value = tournament_base_cost
							multiply = activity_cost_scale_by_era
							subtract = tournament_base_cost
						}
					}
					multiply = tournament_activity_cost_discount_value
					desc = tournament_activity_cost_discount_barracks_desc
				}
			}
			if = {
				limit = {
					factor_zero_if_entitled_to_freebie_activity_trigger = yes
				}
				multiply = 0
			}
			min = 0
			if = {
				limit = {
					is_ai = yes
					has_character_flag = tournament_ai_override
				}
				multiply = 0
			}
		}
	}
}

As written in game/common/activities/activity_types/tournament.txt.

Source: game/common/activities/activity_types/tournament.txt, common/activities/intents and the English localisation, Crusader Kings III 1.20.0.3. Option texts are the game's own; costs are shown as the script the game evaluates.