If you are looking for a no-frills, dog friendly beach in New Hampshire, then Foss Beach in Rye is a good place to visit. This is a town owned beach, so unlike Jenness State Beach, dogs are allowed on the entire beach from the hours of Sunrise to 9:00 AM and 7:00 PM to Midnight, the Saturday before Memorial Day through the Saturday after Labor Day. During the off season, dogs are allowed at any time. Foss Beach is a long stretch of beach that runs from the Rye Harbor State Park, along Ocean Boulevard just past Washington Road. Access is via wooden ramps along the loose gravel stone wall, and free parking is available along Ocean Boulevard.
The great part about Foss Beach is dogs are allowed to run off-leash as long as they are under voice control. The down part of Foss Beach is it is a very rocky beach. If your dog is prone to eating rocks, this may not be the ideal beach to take him. However the rocks are also a plus side to this beach. Most people prefer the smooth sands of Jenness and Wallis State Beach, so this beach tends to be less crowded. But be sure to check the tide chart before you head out! Foss Beach virtually disappears during the high tide. There are no lifeguards on duty here, and no public restrooms. However, if you are looking for a New Hampshire beach where dogs are allowed to run off leash, then Foss Beach in Rye is a very dog friendly beach.
2017 Update: Rye recently enacted a very steep $1,000 pet-poop penalty for those not cleaning up after their pets. It is now considered a class B misdemeanor and a conviction carries a fine of up to $1,000. So please ALWAYS pick up the poop, so that all dogs may continue to enjoy this great beach.