One Thursday a month, we have "Museum Night", which technically isn't a street fair but an evening when the museums (all within a few blocks of each other in the downtown) are open late and free! It's very popular, there are a lot of people going from one place to the next, and I'm sure the restaurants and shops benefit, too.
Memorial Day weekend, there is a gigantic street festival that is actually down on the riverfront (not surprisingly, called Riverfest). If you watch your pennies and buy the tickets early, it's a good deal. There's also a shuttle system to the downtown area.
Little Rock just doesn't seem to have a lot of ethnic neighborhoods, being a smaller city, but there are fun festivals in the Hillcrest area (what passes for a non-straight neighborhood here).
There's also events in Wildwood, which is a pretty park near my home. That's more for classical concerts, opera, and ballet and of course, the flowers.