I love taking the Concord Coach bus from Portland to Bos. The one for NH (Boston Express) appears to be the same company essentially. A clean comfortable Coach bus and a easy 1 hour ride to Boston South Station which gives you plenty of direct subway or other methods around the city. Seems only 1 daily departure from Manchester, but every 30 minutes from Londonderry. $27 round trip

Or drive to a MBTA commuter rail station (like Lowell MA) and take that into the city. Leaves every :45 to an hour and brings you to Bos North Station in about 45 minutes. $10.50 each way, or $10/day on weekends from that station (cheaper if you go to a closer station, but make up for it in reduced gas cost).