If you feel like walking you could visit  Strawbery Banke, the way Portsmouth was at the turn of the century.  Try Prescott Park for a stroll, pretty gardens, on the river.  And, if you want to take a cruise, take the trip to the Isle of Shoals.  These rocky islands are divided along the border of Maine and New Hampshire.  You get a narrated trip down the river, the boat stops at Star Island where you can get off and look around for about an hour and then returns back to Portsmouth.

 ** Note:  The original information for this thread came from the the forums.