I was at the Barney's outlet yesterday and they had a bag that was perfect for this. It was like $60 and awesome. If you have one nearby, you should definitely check there.
I've always loved LLBean tote bags for weekends away and they're really popular at the colleges I have been at... There's always the classic boat and tote (with monogram of course):
Or a leather messenger:
Plus there are so many other great variations in different colors, tweed, leather, etc. But if she's not preppy, I think that the suggestions for TJMaxx, etc. are all good ones.
Oh, and Lesportsac can make kind of fun weekend bags that are very reasonably priced in lots of different patterns: