As a British transplant to Kansas City, who has now caught the meat smoking bug, you can't beat KC BBQ! I've eaten my way around a lot of the more popular joints in town.
Best ribs (and fries): Rosedale BBQ. Truly the best tasting, leanest and moistest fall-off-the-bone-est ribs I've ever had. You REALLY don't need the sauce - they're SO tasty without. A true sign of quality. Dinner (rather than lunch) has always produced the best ribs for me. Fries MUST be cooked in something very lard-y. So crispy on the outside, softy and fluffy in the middle. Screw the diet, you GOTTA try this place for ribs and fries.
Best sandwiches: Arthur Bryants. The "downtown" location is an institution - even visited by celebreties and ex-presidents! Order a sandwich and fries and you will have another meal for the next day right there too! HUGE! Fries, in complete contrast to Rosedale, are the soggy soft kind, but OH so good too. Ribs no-where near as good as Rainbow. Bryants location out by the NASCAR track has comparible food, but somehow it just doesn't taste the same in the yuppified location!
Avoid at all costs: The yelled "HI, MAY I HELP YOU" from Gates, and the hugely variable food quality and and frequenty dried out ribs.........
BBQ. It's not just for breakfast, lunch, and dinner anymore.......