Hi nat, what a lovely idea. Naughty's got a great solution there too!
You could create a picture scrapbook, which would be cheaper. Write captions with the photos, and decorate it to suit her and you! Go on a day out together, take lots of photos (if she asks why, just say it's cos you want some for going away or whatever), and then pick the favourite ones out for the scrapbook. Similar to this is a story book, with pictures, memories and items that symbolise shared private jokes or life experiences.
You could use one of the online sites like snapfish.com to get something made from a favourite picture, alternatively.
You don't sound at all stingy. I have been a Uni student for almost 3 years, and moved out at 17, so I know how important it can be to be careful with money!
Have a fab time when you go, and enjoy it lots! xx