in England, it usually means grilling. As for a restaurant that actually specializes in it, that would be unheard of and downright un-english!

I think that most of the southern US has the barbecue thang cornered. Certainly aorund here in Austin there are more 'cue joints than you can shake a smoky stick at.
Of course they all claim to be the "best in the world", but that is uaully a pretty small world view!