My thoughts. Hmm, best hospital by a fair amount is Dartmouth Hitchcock. The second and third best are probably Catholic Medical Center and Elliot, both in Manchester. There are smaller but decent hospitals in Nashua, Concord, Portsmouth, Derry... and a few others that get much smaller.

An acre of land and good schools rules out Manchester and Nashua themselves but one of the nearby suburbs would work and then go into the city for nightlife.

Best nightlife is probably... Portsmouth but Manchester has a fair amount as well. As do the other larger cities and towns like Concord and Nashua and Keene I've never lived near Lebanon/Dartmouth but it's a college town so I'm sure it has it's share.

For schools you can look at something like https://www.usnews.com/education/best-high-schools/new-hampshire/rankings . It has the usual suspects of higher wealth communities, unsurprising. I will comment that if you value more diversity in the student body you can get a good education in one of the larger cities like Manchester or Nashua you just might need to pay more attention as a parent to what is going on. I brought my kids up in Bow though so I should not really talk in that regard.

Stores and gyms are pretty much all over the place so not much of deciding factor.

Safe area? Well, compared to any major urban area everywhere in NH is pretty safe. But, clearly it is safer in less dense more rural areas than in cities, but those areas also don't have much night life so... balance to your taste.

You don't mention cost at all in your preference. If it really is not a factor for you I'd probably consider Portsmouth or the area. Durham maybe, great school system there and also a college town. Close enough to Portsmouth to get there for a bit more urban feel and it's great restaurants and a lot of cultural activities associated with UNH right in Durham. Exeter would be another option out that way for the school system.

The interior areas are less expensive to buy in. A suburb of Nashua, Manchester or Concord may appeal to you. I suggest Hollis, Bedford or Bow as possible good choices.

Then in the upper valley, Hanover or Lebanon look like good options.

There are a lot of towns right near these ones that would be great too... depends on how highly you want to factor the school system and what your budget is for housing and how that balances.

The rambling response brought to you by not going to sleep hours ago like I should.