gb, Blowin' Smoke at 514 Martin Luther King, Jr. Blvd (912-231-2385) is probably the best downtown. Pretty damned decent. http://www.blowinsmokebbq.com/
Some folks like Wall's, which is a little hole-in-the-wall at 515 E. York Lane (912-232-9754). Not bad at all, either. I like getting a sammich from them at lunch time and sitting out in one of the nearby squares to knock it off. See http://www.savannahoffthebeatenpath.com/Food/wall%27s_bbq.htm
One place downtown I haven;t tried is Angel's at 21 W. Oglethorpe Lane (912-495-0902). See http://www.angels-bbq.com/ I do need to try that place someday.
You comin' for the Rock 'n' Roll Marathon? In any case, hope you enjoy your time down here.