I needed some information out of someone so I had to out drink him. After a few mugs of ale, my vision started to blur and the room started to wobble, but he still wasn't ready to talk so I had a few more mugs. Eventually he caved, but by that time I was pretty far gone. Now I'm seeing double and stumbling all over the room. I'd hate to try to fight in this condition. What can I do to sober up? Will I get better over time, or is meditation the only option?
The only option beside meditating is drinking a Wive's tears potion, you can create one using Rebis, Quebrith and Aether. If you don't have one you need to stumble to the nearest campfire.
You should always have a Wife's tears potion in your inventory, there are two story-related occasions where you have to get drunk and a few more optional ones.
If you don't have the Wife's Tears Potion handy, you can drink more, and pass out, which will result in waking up sober. Alternatively, if going to the nearest campfire will take forever 'cause Geralt's drunk, draw a sword, and you will find your movement speed will increase quite a bit. Also, sideways movement is faster than straight movement.
There are talents that mitigate the disadvantages of being drunk in combat, and there's a good chance you've taken at least some of them.
Lastly, I once was drunk and went afk for ~15 minutes and Geralt was sober when I returned, so possibly time alone can get rid of it... although it is possible he simply passed out and then woke up in the time I was gone or something.