Where are you staying? What are your interests? There's a lot to see and do in NH.

Off the top of my head I'd say drive up 93 to Littleton. See the Old Man of the Mountain former site. The Flume hike is awesome. Echo Lake is cool to see as well. Littleton is a cute town. Back south towards Lincoln. There's a cool tower to climb at the Indian Head Resort. You can see the Indian Head in the Mountains from there.

Lincoln is a cute town too.
Kangamagus is a must do. Lots of places to stop and see nice things.

North Conway is amazing. Great restaurants, cool stores.

Jackson covered bridge.

Lots of hikes, little waterfalls in the area as well as very challenging hikes

See Mount Washington. Auto road if you dare.

Storyland if you have little kids is adorable.

Lakes are awesome. Lots of great beaches to swim in. Rent a kayak or canoe or a motorboat if you can.

The seacoast is lovely too. Some very nice beaches. The weekends can be busy at some of the bigger beaches.

Portsmouth is fun. Amazing restaurants, shops, etc. Strawberry Banke is interesting. See a show at Prescott Park, take a ride to the Isles of Shoals.

I could keep going. So much to see for such a small state. Everything is pretty drivable and accessible.