First Watch is rabidly popular in the Kansas City area. My mom loves the place, but you have to go EARLY to avoid a significant wait for a table.

As for BBQ: Arthur continues to thrive on its name, but really doesn't deliver a great product anymore. Fiorella's has stepped up as the best BBQ experience in town, IMHO. I still like Gates for a quick lunch sandwich (I like their spicy sauce), and even KC Masterpiece (corporate as it is) does lunch pretty well. But when I want to sit down and get acquainted with a full slab and 4-5 beers, Fiorella's is tops for my money.

To escape the BBQ/steak genre, go to Lidia's near Union Station or Frondizi's on Main Street. Both of those are good Italian joints.