I'm a leader from Cerberus.
I have a mansion that I dedicated to building my own custom events of which some are held outside. The FC house lacked the required slots to do this while still looking nice.
The most popular ones:

Garden jumping competition (to the roof or around the garden or house).
Decorating (you assign a room to this and provide items members may use).
Fashion event (you name a theme and style and members have to get close to that within a certain timeframe. They get a small amount of gil for each round to find the stuff with NPC's or buy on market).
Find the difference. A Cross setup showing 4 sides. All items show the same item but on 1 side that item will be in a diff position. 60 items on each side (items that you can name easily), 30 minutes to find them.
Hide and seek (custom rules), Separate in teams. the host of the event hides in a large area. 1 person from each team searches. If 1 person finds the host he/she will relocated. If each player of 1 team is able to find the house, they win the round.
Prizes are gil based or mog station codes for items or emotes. I invent games like this all the time on the go cuss I enjoy entertaining people.
I have a new FC since shortly so I plan to restart this soon, so if someone is interested... find <<ECP>> Eclipse on Cerberus/Chaos. We also allow members to post their own events on discord for others to join so no one has an excuse when there's nothing to do