As of October 2016, there were approximately one thousand restaurants in Wichita. This makes for a lot of competition. I looked online to see what type of barbecue restaurants there were and there were not that many. Amazingly the reviews online are sparse but helpful. Here are three restaurants that have rated at least a four-star rating.
http://www.croniesgrill.net/2018/11/15/great-barbecue-in-wichita-ks/