Take route 90 along Lake Erie (go around Cleveland if you’re that far west in OH) through the PA corridor to route 86 in NY (PA roads suck and are always under construction). Gas up in the PA corridor and again in the middle of NY. Take the southern route through NY and swing north to the Mass Pike (route 86 to route 88 to route 90 south of Albany), skirt Worcester using 290, take 495 past Lowell and then take 125 north into NH and then take your pick. There are actually a bajillion ways to get to Salem, NH once you get close, none of them involve cities.
I lived in SD and we visited family in NH (Salem and Chester, in fact) a few times each year. It was easier once we moved to upstate NY, but the route from there was the same. Now we live in NH once again, so we’re coming from a different angle.
Anyway, that’s the route I’d take - minimal cities, reasonably good roads, plenty of services along the way, although, if you’re driving in the dead of night, you might want to plan your fuel stops accordingly.
The Southern Tier Expressway, I-88 through southern NY is absolutely GORGEOUS.
I LOVE that drive.
Corning is a good place to stop. It’s a small city but very nice. And there’s the Corning Museum of Glass which is worth the stop at. it’s right off the interstate. Very easy to find.
True about PA roads always being under construction.