In Kansas City, everyone has heard of Bryant's but since ol' Arthur has passed away, it has been, somewhat, an acquired taste. When visiting, try Gates ( a number of them all over town), and Fiorellas Jack Stack, followed by Smokehouse (on N. Oak), Antioch (also up north) as well as the usual Haywoods, Quicks, Wyandot, Zardas, and Rosedale.
Currently my favorite is Fiorellas in Martin City. But I change my mind every six months. And of course, in KC we have Bar B Que Ribs of every variety, sausage, beef brisket, pork, turkey and almost anything that will fit in an oven or smoker. So it depends upon your personal favorite in meat as to which place you will like the best.
Kansas City has some great steak houses as well. When you are here next, run me down and we will go to the Plaza III Steakhouse and you will definetly remember it. It has only gotten better with age.
The only think better than the steaks at Plaza III are the hash browns. And I'll agree with you 110% on Jack's Stack in Martin City. If you change your mind about barbecue then you can mosey on down to Jess n' Jim's.