A.S.
Most restaurants have at least one or two good veggie options.
Jerusalem Cafe is great.
Bluebird Bistro (17th & Summit in KCMO)is a locally owned place, great veggie options, with a few meat options, everything is organic. It can be a little pricey, but a cool place to check out. Here's their site: http://www.bluebirdbistro.com/
Genghis Khan Mongolian Grill (39th & Bell in Westport) is another great option. Locally owned, and you can make your own food or order from a menu. The veggie soup is FANTASTIC!
The Blue Moose (71st & Mission in Prairie Village) has some good options, you can order a bunch of yummy vegetarian sides and combine them into a meal.
75th Street Brewery is locally owned and a KC landmark. They have a few vegetarian options, a good pasta, an OK veggie burger, and a few other sandwiches/entrees. Plus, you can taste test some local brews!
Houston's (though not locally owned...) has a great veggie burger, my favorite. There's one on the Plaza.
Here's a website that lists some more restaurants: http://www.vegkansascity.com/restaurants.html