For new school/competition team style BBQ- I like Q39 near Westport quite a bit. Meat and sides are both good, nice table service style place with a crowd that will answer the question "Who the hell is filling stadiums to listen to that little weirdo Ed Sheeran?" Slap's has great meat that is cooked to temp great, but lacks seasoning. I still really like it and as someone already mentioned, sides are just ok.
For my old neighborhood style, ugly-delicious, classic joint bbq, I love LC's out farther south near Raytown the best. Most famous for their burnt ends, but everything is usually really good. In that same style, the original Bryant's (don't go to the one by the NASCAR track) CAN be my absolute favorite bbq in town....it's hit or miss, but when it's on it's on. I don't eat a lot of bbq out because I cook competition style at home, but all these are picks for when I'm in the mood.
Man, if you were ever in KC longer, the legit Mexican food here is top tier. Got a new-to-me carnita place that is maybe the best pork I've ever eaten, and a chef friend of mine turned me onto a place that specializes in stuff mainly found in Mexico City that I've dreamt about all week. Pambazos, Tlacoyos, Sopes, deep fried friggin' tamales......damn.
Edited to add: If you happen to be near the Crossroads area tonight, follow the cigar smoke to the restaurant patio at 1924 Main for the premiere smoking and drinking club in at least a 2 block radius.