Hi George,
I was just in southern NH for about a month. If you are in Portsmouth area you will be real close to the Cocheco in Dover. Park near the dam and walk downstream. I’m not sure how it will fish in the summer and it is a stocked fishery, but the water is beautiful and we caught browns and rainbows. This would be real close to you if you are in Portsmouth. I’ve fished a little up in the Whites, but not extensively, you should check out the Androscoggin near where it crosses into Maine (Shelburn/Gorham area) and the Connecticut River up around the Connecticut Lakes. I would check out all of the designated fly-fishing only spots in the state, I have been to a couple of the ponds and they fish really well (albeit spring and fall).
There are a ton of other opportunities around the state. If you are in Portsmouth there should be some good summer striped bass fishing in the Great Bay or over the state line in Maine. They release brood stock Atlantic Salmon into the Merrimack River near Concord a couple times a year. And there are tons of small warmwater lakes and ponds filled with panfish and bass. I grew up near Nashua schlepping a canoe all over creation fishing for bass, if you find yourself in the Nashua area with a canoe and want a couple of spots let me know!
Good luck,
Mike