NH has coast line and several islands. It is known for it's lakes. But yeah, 2 towns north of NH (into ME) there is York with 1 of the most popular beaches in Maine and another beach with free parking. Just 45 minutes north of NH is Old Orchard Beach, Maine's most famous and popular beach. So while it's not technically in NH, it's closer to quite a bit of the NH population than it is to many of the folks in ME.
Just south of Seabrook Beach in NH is Salisbury Beach in MA. Crane Beach, MA is only 35 minutes south of Seabrook, NH.
About the NH beaches on the ocean, they are known as the cleanest beaches in the United States, with 2 of it's ocean beaches having the amazing level of 5 out of 5 stars!
http://www.npr.org/blogs/health/2013/06/26/195896606/a-look-at-the-nastiest-and-cleanest-u-s-beaches
New Hampshire also has many lakes with beaches. In fact, I think there might even be a pond in Grafton, NH with a beach. I might have even swam there before