For an inexpensive lunch, try New Chinatown on 20th Street. If you're with a vegetarian, they have a fairly expensive selection of tofu dishes. Also, Mellow Mushroom on 20th at 13th Ave. is a decent place for pizza. Decent beer selection. Even better beer selection (and OK food) in 5 Points South is J Clyde's in the Cobb Lane Alley (between 13th and 14th Aves, I think). Good people watching on a Friday evening at Dave's Pub, as well.
If you're willing to venture out, about a half-mile out of 5 Points is The Garage, a funky bar with a courtyard that doubles as an antiques/stoneware kinda place. It's off Highland.
The best bet for BBQ in Five Points area is Dreamland. Located at 14th Street and 14 Avenue South. They are known for their ribs and sauce. The sauce is vinegar based with loads of pepper. Yum! They're an icon in these parts! They have a pretty limited menu though. Google will find a link to their menu.
The only other selection of BBQ in the FPS area is Jim & Nick's. Very good, more variety in their menu, good smokey flavor, wonderful cheese muffins!
There are quite a few great restaurants in the FPS area, it just depends on your cuisine and price point preferences. High end/Fancy/Expensive = Highland's Bar & Grill (New American Continental), Hot & Hot Fish Club (New American Continental) and Bottega (Italian). Moderate = Chez FonFon (French Bistro), Bottega Cafe (Italian), Ocean (seafood), Surin West (Thai & sushi). Cheaper (but not cheap) = 26 (varied menu but with a great vibe!), Cosmos Pizza (self explanatory). Cheap = Purple Onion (fast food Middle Eastern).
Most of these restaurants have been discussed on the South board many times. Do a search here and on the web. Most of the higher end places have website with menus for your perusal.