Mystic is too far for "a couple of days with a rental" from NH. It would be a whole day just for that. Do your time in Boston try and catch a Sox game at Fenway even if you don't like baseball or the Sox just to see the ball yard. Faneuil Hall is a quick take, the Constitution for sure, the Boston Common, Bunker Hill Monument, if you're a museum type the MFA is awesome or Isabella Stewart Gardner Museum, go through the Peoples Republic of Cambridge to check out Harvard and MIT, and stop in the North End for lots of food. I'd also say you're right in a stop in Portsmouth on the way and you can do a short stop in Gloucester on the way to Boston.
 
Just remember drivers in Mass aren't called MA***s for nothing. To most around the city using your blinker is a sign of weakness. And the roads don't really go where you want them to, the cow paths that were made into roads are just silly, signage is pretty much nonexistent, and a sign that says "north" may actually be on a road that heads "south" but ends sort of north.

Ah, my neck of the woods, back in the day...

Yeah, Mystic CT. is definitely a nice visit, there's also Old Sturbridge Village and Lime Rock Park.  When in Boston, the Freedom Trail, visiting the Old North Church and cemetary (many of the 'big names' are there, the Constitution Museum if not the ship itself and have lunch at Faneuil Hall Marketplace or in Chinatown.  If the weather's good, take the ferry out of Woods Hole to Martha's Vineyard for the day - get t-shirts at The Black Dog - I used to frequent it before it got trendy.

You must try to make it to Newport, RI - the 'industrialists' had their summerhouse mansions there - The Breakers offers tours.  The original '60's 'scary soap opera' Dark Shadows was also filmed in an awesome house - mom didn't watch it, but my friends mom used to.  We loved it as kids.  I used to ride my bike down to Newport virtually every day from my apartment in Riverside - a decent ride, but the beach was great.  Tennis Hall of Fame used to be in Newport also, and if you get a hankerin' for some good ol' clam chowda, The Black Pearl restaurant in Newport is where you'll get a good one.

Mt. Washington is a pretty area, bring a warm jacket as the weather turns quite suddenly (a day hike can be deadly), Southern NH has also some nice drives through Amish country between NH and Maine. 

Have fun!

Mystic Seaport ,CT. Old ships, shops, sort of a nautical Williamsburg. Then of course in Boston is the USS Constitution (Old Ironside) . I think it is still in drydock but you can still go onboard. In New Hampshire you can to the top of Mt Washington and hope for one of its famous windy days

OT - where to visit when in New Hampshire/Boston in July? We are going out to drop daughter at Uni New Hamp for a volleyball camp in the middle of July - the boy (15) n I will have a couple of days with a renta car so we can bop around. Boston, Portsmouth, any suggestions? I'd like to visit the historical stuff, boy doesn't really care except for the constant need to eat....