Sunday lunch near KCI
jdl98 stole all my answers! Ixtapa, Swagat, Tasty Thai, and Malay Cafe are all excellent choices. All also have plenty of vegetable options. Ixtapa's Vegetarian Chile Relleno is one of my favorite things to order. (FYI: It is not the heavily breaded monstrosity you see on most menus.)
Please note that none of these places are very appealing from the outside (save Swagats), but are very warm and inviting once you cross their thresholds.
Well, until I saw the thing about vegetables, I was going to suggest Cafe Wetherby at the airport Hilton. Their barbecue team (Munchin' Hogs) is award-winning and it is super convenient to get there from the airport. They do have a full menu, but it isn't *especially* gifted with vegetables.
Here is their lunch menu