I don't know about Wichita but about an hour east in Topeka is what I believe is one of the best BBQ joints in America. It is called Boss Hawgs. It is run by Hank and Elizabeth Lumpkin. Hank and Elizabeth are strong competitors on the professional BBQ contest circuit when they can get away from the restaurant. They have been kinda tied down lately because they opened a BBQ sports bar next to their restaurant. If you get a chance to go over, ask to talk to Hank or Elizabeth while you are eating and tell them that "RibDog" sent you.
Check out their website at Http://www.bosshawgsbbq.com.
P.S. - These people really care about serving their customers!