Re:One Meal in Kansas City
ayersian makes a fine point about your handle including bbq, and as such, your one meal might likely be a legendary KC BBQ joint.
I say, even with that caveat, your ONE MEAL should be at Stroud's. I would guess that Stroud's is in my Top 5 of ALL-TIME, as far as Roadfood restaurants go. I couldn't say that about any of the bbq contenders.
If I were to rank the 'cue places, my own order (of the places mentioned already) would be:
Oklahoma Joe's - I always seem to like this place more than BB and WJ, but I will tell you that on the occasion of a trip to KC where I had time for one meal, I drove to Stroud's to find them closed (yeah...I know...a shocker....didn't realize that they weren't open for lunch during the week), and turned around and went to OK Joe's - the original location, in the gas station in KCK.
LC's - If only for the burnt ends. The second best thing on LC's menu is their fries, but my personal opinion is that all of the other meat selections and sauce are better at Oklahoma Joe's. It is less convenient to get to and not in the best neighborhood, if that is important to you.
Gates' - I was surprised by how much I really liked Gates. The food was better than I had envisioned, and it is probably the most accessible (ease to get to, parking, spacious, etc.). I would absolutely go back.
Arthur Bryant's - I won't go so far as to say that you shouldn't ever go there, as mentioned above. There was a time when if I had time for only one meal in KC, it would have absolutely been at Arthur Bryant's. That time is gone. That said, from an historical perspective, I think it is a worthwhile visit - just go with lowered expectations.
Lastly, the one place that others have not mentioned - but, if your one meal is breakfast, you should forego all of these recommendations and go to Niecie's and order the pork chops fried right!
Keep in mind, to get to any of these places, you'd likely need to have your own car. Kansas City is not a very public transit-friendly town for out-of-towners.