For my weekend trip to Kansas City, I tried searching the Chowhound discussion boards for restaurant ideas and found that most of the threads other than the BBQ ones were a bit outdated. For future reference, if anyone needs some itinerary ideas, I thought it would be helpful to report back on the restaurants I did try. As an fyi, I was pleasantly surprised by how good the food in Kansas City was, and definitely on par with some of the places in NYC.
For more context and pictures, you can read the extended version here: http://bit.ly/1h9cwFF
BBQ - Oklahoma Joe's totally lived up to the hype. The Z Man Sandwich and the ribs in particular were amazing. Totally worth the 40-minute wait in line on Sat, which is actually quite reasonable. Some people worry about the seating situation, but tables turn around fast so you'll be able to find somewhere to sit if your party is 2-4 people
Brunch - Bluestem and Room 39 do a great job of serving solid American breakfast classics. I liked the brunch at Room 39 slightly more, because the flavors were a little more interesting and memorable, but you can't go wrong at either. The artichoke toast at Room 39 was one of the more unique and tasty brunch dishes I've had in awhile. Their bloody marys and huevos rancheros are good, too.
Mexican - The tacos at Bonito Michoacan were awesome, and very budget friendly at $1.49 each! The chicharon taco was my favorite. If you're okay with eating in a Mexican grocery store and don't need the fancy margaritas/chips/guac experience, then definitely check this place out. The restaurant also has a bakery across the parking lot, which serves gigantic Mexican pastries. Leave some room for the generous wedges of cheesecake.
Coffee - I've had the best black coffee ever at Oddly Correct. This is a very hipster, serious-minded coffee shop, not unlike the places in Brooklyn or Portland. For something more laid back, you can try Mud Pie Vegan Bakery and Coffeehouse. Their black coffee isn't as good, but their milk-based drinks are tasty, as are their vegan desserts.
Cafe Sebastienne - If you're having a museum day, definitely have lunch at Cafe Sebastienne in the Kemper Museum. This isn't boring or weirdly conceptual museum food. The grilled fish tacos I had were hearty and flavorful, as were the mustard-curry shrimp.
Extra Virgin - this was the only restaurant I was disappointed by. I had high expectations for the duck tongue tacos, but there was too much shell and onion and not enough duck flavors coming through. I've had better fancy tapas elsewhere.