I met a girl on a weekend away and got a photo with her, problem is I was v-drunk and can't remember her name, how do I find it out?

Take the photo to the places you were at, the place you meet her and ask them if they know her

I would but its miles away from my house, do u have any other ideas?

Make a copy of the picture and mail it with a letter including your telephone number and requesting information to people at the establishments you went to. If you want to speed things up (people forget quickly) get their fax number and send the info. Or hire someone to go to those places with the picture to ask for you.