So I was out drinking last night…how to remove a tattoo

You can get your stuff back. When you wake up, you should be next to Rudy, who will tell you that you don't want to remember what happened last night. Bribe or intimidate him anyways and he'll tell you that he's not the one to ask, but that the madame Marlot should know. Find her in the basement of the inn(the building where the notice board is located). When you head down the stairs to the basement, and go into the more open area(where there are/were people fighting), you'll notice a door by the corner. This leads into another hallway. When you go through that door, there's another door to the right leading into an elegant bedroom. This is madame Marlot's room.

I believe she also requires to be bribed. After you've done that, she'll tell you that you should go speak and apologize to Ves. Visit Ves in Roche's house(the place where you got drunk to begin with) and she'll tell you the full details of your night and mention that your stuff can be found in the chest by the window.

It seems this is the only path through the quest; you must bribe or intimidate Rudy to get your quest directives. You can't skip straight to Ves and get your stuff back since she has the key and you need to follow the quest to get the dialogue option. Rudy's the guy with the fishing rod right by where you woke up.

As of Patch 1.2, the bribe option always remains open even after bribe failure, fixing the bug where people could not progress after failure on both intimidation and bribery.

Not exactly sure where you are but I guess this:

Amphitheater area is accessible from the hallways leading out the far side of the town square. Along the amphitheater, head to the right and you'll find a room where gargoyles attack

Here is full quest guide

Map

Video guide