Another idea would be Union Pizzeria - upscale pizza (and other entrees) with a great music room in the back, called SPACE.
1245 Chicago Avenue (one block east of the Dempster El stop)
Evanston, IL 60202-1337
(Society for the Preservation of Art & Culture in Evanston)
Excellent suggestion. It's worth adding, SPACE features some relatively big-name musical acts, with the opportunity to see them up close in a small venue. Check out the calendar on their website and see what strikes your fancy.
Some words of caution about the Union/SPACE combo, though. As you can see on the website, you can order pizza at Union and bring it in to SPACE to eat. I would strongly advise not
doing this, unless you like eating out of your lap. The reserved seating at Space has four people at a table, but the tables are tiny (my recollection is they are rounds maybe a foot in diameter), barely enough for drinks; even worse, if you have general-admission seating, there are no tables at all. If you want to eat at Union before a show, allow plenty of time; waits of half an hour to be seated are fairly common, and they don't take reservations. (I ate there before a show and did not like their pizza at all, but I know some other people like it, so there's that too.)
Other restaurants within a block of SPACE include Blind Faith (vegetarian) and Dozika (pan-Asian). Expand the radius to half a mile and excellent choices include Oceanique (upscale seafood), Cross-Rhodes (Greek), Kuni's (sushi), Campagnola (contemporary American and Italian), Lucky Platter (eclectic), and Prairie Moon (California-ish).