The Wanderer's Palace is a great dungeon to run as a fresh 50. Not only will you be able to grab some ilvl 55 gear, but some of the coffers in this dungeon drop materials used to craft the weapon for your Relic Quest Line.
After the first boss, you will need to deactivate Nymian Devices to open the doors. While these are usually near the door, in the maze section, these devices are spread out. One is at the start, one is in the middle, one near the door in the north, and the final device is next to the east coffer. These are marked on the dungeon map.
Clearing this dungeon will reward 100 Allagan Tomestones of Philosophy and 30 Allagan Tomestones of Mythology.
Tank the Keeper of Halidom facing away from the group, either in the middle of the room or against a wall. This will prevent Beatdown and Moldy Sneeze from hitting anyone other than the tank. The healer should remove the Reduced Immunity debuff from the tank after each Moldy Sneeze.
Everyone should spread out around the boss so only one person has to move to avoid Inhale. If you do get sucked in, move away from the boss immediately, as it will always follow up Inhale with Goobbue's Grief, poisoning all nearby targets.
Finally, the Keeper of Halidom will place a circular ground indicator under a random player. Move out of this to avoid Moldy Phlegm. If someone is hit, the healer should Esuna the Reduced Immunity.
Side-Note: Both times I have tanked him in the back-left corner, he has never used Inhale. I plan on testing this a bit further to figure out if that was luck or not.
This boss drops 20 Allagan Tomestones of Philosophy.
Throughout the fight, the Giant Bavarois will cast Fire as its primary attack. While not always necessary, if you find yourself low, you can move behind the boss during the cast to cancel the ability.
Occasionally, 3-4 colored Bavarois adds will spawn. If possible, you should AoE these adds down quickly. If you do not have strong AoE, kill the Blue Bavarois first to stop the heals, followed by the Yellow, Purple, and White Bavarois. If the healer is a White Mage, I highly recommend putting up Cleric Stance and casting 2-3 Holy spells to quickly take down the adds. The healer should also make sure to remove Paralysis/Heavy quickly.
In addition to the adds, Giant Bavarois will also emote "The giant bavarois's eyes focus on a single target" and begin to chase a random player. During this time, he will cast Fire on that player and, after a few seconds, will attempt to use Amorphic Flail on them. Just run away when he focuses on you and you should avoid the flail. Even if the boss is not chasing you, do not be in front of him, as the Amorphic Flail can still hit you. If the adds are still alive during this, they will attempt to flail you as well.
This boss drops 30 Allagan Tomestones of Philosophy.
While fighting the Tonberry King, the tank should position the boss in the middle of the room and avoid moving. Any Tonberry, including the king, will use Scourge of Nym on you if you have aggro and are outside of melee range.
Occasionally, small Tonberrys will spawn near the outside of the room and slowly start to walk toward the Tonberry King. A good burst DPS should focus on killing them each time they spawn. White Mages can be useful here with cleric stance up, as they can two-shot them using Stone II. Each time a Tonberry dies, it adds a stack of Rancor to the boss. This stack is removed each time Everybody's Grudge is used. Avoid letting this stack more than three times, as it can easily one-shot the tank.
Once the Tonberry King is around 25% HP, he will surround the room with Tonberry Slashers. These will take a step forward every 15 seconds or so. You should move close to the Tonberry King and ignore the Slashers. Continue killing the Tonberrys if their damage is a problem and finish off the Tonberry King.
If you move close to a Tonberry Slasher, it will use Throat Stab on you for over 2000 damage. Also, if you accidentally attack one, you will likely be one-shot by Scourge of Nym.
This boss drops 50 Allagan Tomestones of Philosophy and 30 Allagan Tomestones of Mythology.