If your girl has played AAA the last 4 years out there you are are not going to be happy with the high school option. Certainly not NH as high school girls hockey is terrible there. In MA you would find better HS hockey but it's still not great. There are a few teams that field decent teams but the majority of the hockey isn't very good. It would be tough to find a really good academic public high school that had a good girls hockey team. There is the academy model or prep but remember all prep hockey is not the same. There are girls prep teams that are absolutely terrible and there are some really good ones. Do you research.
Reach out to either the Eagles or Wizards programs - their coaches now the landscape very well - as demonstrated by their track records of success. Either program should within 15 minutes be able to guide you in the right direction if you are looking at prep - most of it depends upon your daughter's academic level as not all preps are the same in terms of academic requirements and hockey programs.
Long philosophic answer:
What is the end goal for your daughter? I ask this because I think its the elephant in the room and plays a big part in answering your question.
For me why do all this hockey nonsense? it's to get into the best college at the cheapest price. So, basically for girls hockey, the best we can hope for is D1 full scholarship to a major university. Harvard is ok too, but no scholarship, still gotta pay.
Let's be real, economically. Girls hockey in it of itself is a dead end. As of now, there is no million dollar NHL contract for her. Other than D1 type scholarships, there is no direct benefit. But social development, character building, etc....sure that has alot of value, albeit difficult to measure. You see some Olympic level womens players, spent thousands on training and lifetime of practicing...and in the end, they achieve a suboptimal pay ratio livelihood. Sure, few also leverage their hockey experience, determination and leadership skills to become private equity managers and make millions.
So, top academic school and lesser hockey...or lesser academic and top hockey?
Nothing is for sure, both these routes are gambles. good luck.
oh: my advice if of any value, I'd say goto a school and team where the kid grows confidence, is most happy and has lots of friends. Cuz in the end end end...its happiness, right?