There's a number of activities you can do in Vana'diel if you don't wanna delve into the usual adventuring stuff for a change! There's plenty of things to do, some of which yield great rewards or fortune as well, so you should never get bored!
The Auction House
The number one thing to do when you want to earn some nice gil! You can sell all your unwanted items and earn a handy price if sought for by other players. Additionally, of course, you can buy things you don't wanna aquire yourself.
You think, Trusts are cool, but you want to have a customizable companion you can design after your desires? Want to have a buddy you can give equipment to and talk with if you're lonely? Then you need an Adventuring Fellow! You can't call him/her to any place you'd like, but it can still be fun increasing the bond between the two of you.
See also: Adventuring Fellow Quest
Crafts and Hobbies
Crafts are actually an essential part of the game and require you to train them in order to skill up. If you invest enough time, you can make a lot of Gil as well. And they look really badass when using certain crystals! Hobbies on the other hand don't require any skill (except for Chocobo Digging) and can be done only by acquiring the necessary tools.
Ballista and Brenner
Ballista and Brenner are both PvP events anyone can participate in. While Ballista is about digging up small stones called "Petras" and throwing them into goals called "Rooks", Brenner is a team vs. team event that requires you to light so-called "Flammen-Brenner" (flame burners) and then protect those flames for a set amount of time.
This special activity - which kinda resembles one certain game franchise about capturing little monsters - is available to all who have the Treasures of Aht Uhrgan-Expansion installed and who have access to Al Zahbi. It's all about capturing monsters in order to let them battle against other player's monsters.
See also: Pankration
Chocobo Raising and Chocobo Racing
Who doesn't love little cuddly Chocobos? Now you got the chance to raise your own one! By caring for it and feeding it, you can make it's stats vary and either raise your Chocobo to be a top racer or to be a top digger who will get more items for you. And if you're really lucky, it might even be a rare colored Chocobo! Also, once your Chocobo has hit adult stage, you can let it participate in Chocobo Racing and become the number 1!
Moblin Maze Mongers and Meeble Burrows
Both activities are available to those with the Wings of the Goddess-Expansion installed. Moblin Maze Mongers is all about building your own dungeon with custom settings and rules while you can delve into underground caves in Meeble Burrows and conduct research expeditions!
Mog Garden and Monster Rearing
Originally only available to those who had the Seekers of Adoulin-Expansion installed, this great feature is now accessible to everyone! Once you enter your personal Mog Garden, you will meet the Green Thumb Moogle who will show you around all the different gathering activities which will give you items. Those items won't be very valuable at the beginning, but you can upgrade them in order to get really rare items! Once you've upgraded your Mog Garden to a certain degree, you will be able to get access to Monster Rearing where you can raise your own little monsters. They can give you items or even global bonuses similar to Moghancements!
Monstrosity & Belligerency
This amazing activity allows players to completely transform into a monster and take control of it, thus being called "Monipulators". There are various types of monsters to obtain and level, so there's a lot of fun hours to spend! Also included is Belligerency which is the newest type of PvP content: In Belligerency, Monipulators battle against regular players for even more challenge.
Wait, you're still here? You haven't tried out anything yet? Then you must be really bored indeed. If you got so much free time, check out those hilarious FFXI insiders: FFXI Jokes