It isn't clear that analise is looking for ribs in the airport, so I'll offer some suggestions (there is pretty much nothing to eat in that airport).

This is from personal experience growing up there; I get back now and again but not all of this will be up to date. The mother of all BBQ review sites for KC is at http://www.rbjb.com/rbjb/guide.htm

What part of the city will you be in? Downtown/near east are going to have the best BBQ. In the 'hood I recommend KC Masterpiece, after that Laura and Emmy's or Jake Edwards.

If you're there on business you'll more likely be in Johnson County, on the KS side (near Overland Park, Lenexa, or Olathe). If that's the case, try Wyandot and Zarda. I don't remember if they have ribs at Zarda or not but it's worth the trip just for the fries and a pulled pork sandwich.

The definitive KC BBQ, however, is Gates'. There are about a dozen all around the city. Great, great food. The second you walk in the door, someone behind the counter will YELL out "MAY I HELP YOU?", likely without interest or eye contact.

Note that none of these places are going to have any pretension of ambience other than lots of fat midwesterners gorging on fantastic BBQ. At gates you'll get a messy slab of ribs between a couple slices of wonder bread and a side of potato salad.

Man, this is making me hungry.

The good news is that I don't think you can get bad BBQ in KC. The places I listed are all fantastic though.

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-alan in sitges, home of the new, improved Si-Re-Do