Better in KC than Topeka in my book.
Joe's Kansas City (formerly Oklahoma Joes) if you want casual. Get the world-famous Zman (brisket sandwich with cheese and an onion ring to top) and fries are some of the best in the world. Ribs are also excellent.
Q39 if you want elevated / hipster. Can't go wrong but start with the wings. Or Local Pig.
Jack Stack if you want reservations / large party / corporate. Wider hours. Open late, full bar. Get ribs, burnt ends + sausage, and the beans are a must.
Woodyard if you want rustic. Would normally recommend higher but there's only one location and it's not exactly on your way to Topeka, but not that bad. Amazing burnt end chili, wings, and the Triple P sandwich.
if you need something else local don't hesitate to reach out.
-P