This is a great alternative to I-93 if you want to get off the highway and relax. Start at the Tilton Diner in Tilton, NH (Corner of Rt 140 and Rt3, just off I-93). After a meal there, follow US Route 3 south and ride in and out of New Hampshire towns, over rolling hills, along the Merrimack River. The road ends in the historic state capital.
The road goes through several small NH towns, with small shops and stores. Between the towns are rolling hills, and a stretch along the Merrimack River.
This is an undulating, curvy road that is great for cruising. Outside of the towns the speed limit stays between 45 and 55, so you can really enjoy the ride. Pavement is decent for New Hampshire, so be aware of the occasional pothole or frost heave, but for the most part is nothing to worry about.
Tilton Diner is a true diner from ages past, where the food was simple and good.
Throughout the towns are small shops to stop at, plenty of fuel stations, and lots of places just to stop and enjoy nature along the way.
Concord, the state capital, offers lots of restaurants. The New Hampshire State House, designed by architect Stuart Park and constructed between 1815 and 1818, is the oldest state house in which the legislature meets in its original chambers. It's gold dome is a sight to see.