Just get north of the Notches and you will be fine, trust me I know, I'm from Jefferson!
All depends on what you want (the following is all opinion) Littleton is your best bet for a town on the grid. Lisbon area is nice, so is Bethlehem. It will get cheaper the farther north you go. Good deals for buying or renting can be found in Gorham & Berlin, even cheaper in Milan, Dummer, and such. Even up near Stark.You have alternatives in that area. Brad is right, Randolph is great, but there are a lot of long-timers there and houses for sale aren't as common as they can stay in the family awhile, when they go up for sale they can go fast.
Subscribe to the Coos County Democrat (online or print, I still get my print down here but an online sub is included with the price) or Berlin Daily Sun.
If by chance you want a college-like town, take Plymouth, its south of the Notches but still in striking distance.
Another option is the Lancaster, Whitefield, Lunenburg area. Lots of houses and apts. for rent and sale. Lancaster is a nice town. Whitefield has a great Common too.
Of course, my fav is Jefferson, but not everyone gets to grow-up in a homemade log cabin that abuts National Forest and can only have been seen by airplane. Some of us are just lucky!
"LIVE FREE OR DIE...DEATH IS NOT THE WORST OF ALL EVILS." Gen. John Stark. "by reason of much foule weather and Extreme Bad Woods to travel in..." From the letter of my Great Uncle, Samuel Willard (accompanied by my grandfather Henry), to Governor Dummer on August 16, 1725, explaining the reason for his return, being instructed to "range all the country", of the Wawobadenik (White Mountains) July 19-August 16, 1725. I am a 13th generation New Englander and proud of it.