Yes, your HS hockey team is dependent on where you live, except if you play for a private school.
There is only AA, A, B1, B2 and C hockey during the winter. Typically MN hockey is a tier above everywhere else in the U>S>, i.e. a MN "B" team could play in a WI "A" and do very well, especially if it's a strong B team.
In the summer, players form AAA squads, some of which are very strong(others are AAA in name only), and can compete with the top teams in the continent, whether it be Chicago Mission, The Detroit teams, or Don Mills Flyers,etc..
It is hard for MN teams to compete in season with teams from anywhere else, as they a have a weird eligibility date.
Some of the top HS teams are very good, but the drain on them by the private schools(i.e. Shattuck) and Junior hockey, whether it be the USHL or CHL, can dilute them. I know of a local HS team that has lost 4-5 top players (would all make the NHL "player to watch" list...one of them a likely first rounder).
There is a wide variance in how good the HS are. The top 8-10 or so are very good, and can beat one another up on a regular basis, and the top 20 are all quite competitive. The smaller schools play in a lower division (according to student enrollment) as do many of the privates(which causes some consternation, as some privates recruit students/hockey players from out of the ranks of the regular HS teams). Some of those teams can still be quite good, however, if you see some unusually high stats from some MN HS prospects, it might be against some weaker teams(ranked below 80th or so.) Typically, the higher ranked teams don't play those teams.
The top 5 HS teams will often try to schedule a game against Shattuck in season. They lose more often than not, but usually have competitive games.