Public Transportation to the Seacoast region is the second best in NH, following the Merrimack Valley region. Don't expect it to be nearly as available as public transportation is in more populous regions. Northern New England is an area of the country where almost all residents own cars, reducing the amount of public transportation available.
By car
There are three major roads leading towards the Seacoast. Interstate 95 cuts through the area, providing the main road from which to enter from either Maine traveling south or Massachusetts traveling North. Interstate 95 is a toll road. From the West Rt. 101 comes from Keene and Manchester and ends at Hampton, providing easy access to the coast, and since it crosses interstate 95, its easy to access other seacoast cities like Portsmouth and Dover. Downtown Portsmouth has a parking garage, and almost all businesses especially hotels have available parking, usually free. In the cities metered parking is available on many streets.
Amtrak Downeaster
Toll free: +1 800-872-7245, (http://www.amtrakdowneast...) The Downeaster runs from Boston MA up through Exeter, Durham the UNH campus, and Dover. The train runs back and forth several times a day, with the schedule available on their website. It's important to buy your tickets in advance if possible, as the train frequently fills in the morning, especially during the workweek.
C&J
Toll free: +1 800-258-7111, (http://www.ridecj.com/) C&J provides bus service on air-conditioned coaches between Dover - Portsmouth and Boston on a regular basis. Check their website for pricing and scheduling.