Hi Trevor, I moved to NH in 1972. Beautiful place to Live, especially if you love outdoor activities like I do. I've hiked all of NH's 4,000' Mts., then went on to do all of New England's, but that was years ago, in my youth (late 40's).
Anyway, as far as investing goes, I've lived in the Seacoast area only, so I can't comment on the rest of the state. But I've watched the Seacoast Cities grow a lot since I've been here. When I first moved here I joked about someday renaming the area "Port Dovsomechester" when it became what I called a "Megalopolis" ( For Portsmouth, Dover, Somersworth, and Rochester) And sure enough that's how I've seen it grow, and now it's hit Farmington (next town up from Rochester) where I live.
As far as investing in Rental Real Estate, I've watched Portsmouth get overpriced, then Dover. Right now I look for properties in Somersworth, Rochester, and Farmington only. People paying the prices they get in the other cities must not be looking for much of a return on their investment to pay the prices they do.
In closing, Warren Buffet even said recently that Real Estate is a good place to have your money right now. And he's right, even here in NH. There are some good deals if you take the time and put in the effort to find them. And what you buy will only get better as we head into the next "boom".