The Kittery Outlets are good for shopping! Some deals and steals there!
I'd only recommend considering this if you're staying for a couple of days because it's two hours away from Portsmouth. This locomotive chugs up Mt. Washington (the "peak of the east," sometimes it's snowing on top even in the summer!) It's about a 3 hour round trip. Really cool experience and chance to see some bigger mountains!
The boat leaves from Rye, NH (there's parking), and will take you to Jeffreys Ledge (maybe ~25 miles out to sea). There's this unique stretch of about 30 miles of underwater glacier remains that created massive shifts in the sea floor. The sea will go from 50 feet to 300 feet deep. This area is nutrient rich and biodiverse. BIG sea creatures flock there: whales, sharks, tuna, dolphins, sun fish. It's an awesome excursion but a multi-hour affair! Definitely worth it if you're in NH for a couple of days. There are other tours that go to the Isle of Shoals too! Portsmouth Harbor Cruise (no parking) or the Gundalow might be a nice boat option too if that's too hefty an excursion! Portsmouth Harbor Cruise has a booze cruise as well :)