There's Pease International right down the street in Portsmouth. They have a really nice grass driving range and practice area, 27 holes (although the "extra" 9 are kind of crap). The other 18 thought are pretty nice. Links style, lots of adjacent fairways and such, good greens, it's a fair challenge.
Down the road there's Sagamore in Greenland. Kind of short course, a lot cheaper, usually in pretty good condition but one hole is right on 95 which is kind of strange. If you aimed towards the highway you could drive it. There's also a Golf and Ski Warehouse in Greenland if you're looking for a good sized shop with a grass range and trackman bays.
The Ledges isn't too far of a drive up 95 from Portsmouth, it's in Maine, about 15 minutes off the highway right over the border.