I can tell you that right now, the Southern NH (Nashua/Manchester/Concord/Portsmouth) housing market is one of the hottest in the nation. A lot of northern Massachusetts people have made their way north of the border with remote work opportunities. It's cooled off a little since the school year began, but I hear that it is still pretty bonkers. Rents are running high, as well.
If you can afford something on the coast of NH, great. If not, Rte 101 is the main East-West thoroughfare in southern NH. I'd suggest taking a look at communities along Rte 4, though. Dover, Madbury, Durham, Lee, maybe Stratham and Greenland-something in that area, if you're looking for easy coastal access without being right on the ocean. Durham is where the University of New Hampshire's main residential campus is, so it's more bike and pedestrian friendly. Dover has a surprising amount of nightlife in its downtown, as does Portsmouth. Using Rte 4 as your home base also gets you closer to Rte 16 and Interstate 93, which are your north/south routes for mountains and skiing. Not gonna lie, the traffic on 16 and I-93 (south of Concord) and I-95 on high-volume days and in tourist seasons can be harsh. But there are a lot of back roads that can be taken, as well. Also, the Manchester airport is easy in-easy out. 20 ish gates, served by Southwest, Spirit, and a couple of the conventional carriers. Don't think I've ever spent more than ten minutes at a TSA checkpoint there. If you need International airports and direct flights, Boston/Logan, Portland Jetport, and even Hartford (CT) are all within a 3 hour drive. And Amtrak is easy to pick up in Boston, too.
As for mountains; from that part of the state, Gunstock and Pats Peak would be the closest. (Technically, MacIntyre in the city of Manchester is closest, but it's too small to mention beyond that.) Sunapee (Interstate 89) and Crotched (Rte 202/9) (both Vail properties) would both be about an hour and a half away. Sunapee is bigger between those two, specializing in mostly blue runs and families. Crotched services the factories in the area with lots of night skiing for the second and third shifters. Wildcat and Attitash are ones I haven't been to in too long, so I've got nothing to add that hasn't been said. Someone here did a fascinating write up on the NH ski areas....Talls and Smalls, I think it was called? Should pop up if you do a forum search.
Not to steer you away from anywhere else you're looking; just wanted to give you my ground perspective as a NH resident. Good luck.