Oh, and in high SES areas, there seem to be a fair number of K-1 players, oddly enough.

In our area (mid-sized city), there are local tournaments hosted by some elementary schools. Those are unranked but fun for a beginning player. DS now says there's no one that provides good competition for him at those, though.

Many states have chess associations and lists of scholastic tournaments, but I think you have to search online for them. I've not seen a master list.