If you are willing to take a short (less than 30 minute) drive up north to Bentonville, one of the top art museums in the country is there:
http://crystalbridges.org/
Well worth a trip, if you even have a passing interest in art museums. I believe both admission and parking are free, as well.
For dining in Fayetteville, Herman's is a local favorite:
http://www.hermansribhouse.com/
Dickson Street (near downtown) is the center of night life in Fayetteville - if that's your thing, head down there on a Friday or Saturday night and sample the clubs, pubs, etc.
Here's a site that looks like might give you some ideas:
http://www.dicksonst.com/