All of the above are good ideas. Definitely head downtown Portsmouth and walk around a bit. Check out Poco's, Stockpot, and the other bars/ restaurants on the water for lunch someday and nightlife too. If you want to see boats, head to Wingaersheek Beach by Gloucester on the weekend as tons of people will be anchored there as well as a good beach crowd.

As far as A/C goes, just check's extended forecast. If it looks real hot and you'll be there for a week, I'd just go down Rt 1 to either Seabrook or Portsmouth Walmart and buy a window shaker for $80. Worth the price vs 1 week with no sleep.