Jenness State Beach in Rye, New Hampshire is a nice swimming beach along US Route 1A. There are changing and rest room facilities on site. If you want to swim or sunbathe without the hustle and bustle of Hampton Beach this is a nice option.
There is a metered parking lot that will fill up quickly in the summer. As of April 2019 the beach parking area is undergoing renovation and is closed off. I expect it will be open for the 2019 summer season.