May-October is ideal in the Northeast quadrant of the US. We don't get lots of severe weather, but icing is always possible in clouds in May or September-October. Cutoff lows are pretty common in May-June, leading to claggy but usually benign IFR weather for a week or so. Farther south, afternoon buildups and thunderstorms are typical all summer long, but can usually be avoided by flying in the early morning. Some days, you just have to give up by 2pm or so, other days things are widely scattered. The main lesson is to not be in a hurry to be anywhere in particular.
If flying to Maine, Portland (PWM) is GA-friendly, and the city has a cute minor league ballpark, as well as lots of good seafood. LL Bean is nearby. Bar Harbor (BHB) is very popular with the Acadia National Park, but it is quite crowded with tourists from July 1 - Labor Day. May or June is a good time to visit before the crowds appear, although in May the mosquitos can be pretty bad in the woods. After Labor day the throngs thin out a bit.
A visit to the Adirondacks (SLK) would not disappoint. Day-hike some mountains and enjoy some wilderness. July-August is my favorite time in the mountains, when the mosquitos die down, but May-June is cool and refreshing (bring DEET). Or on your way through Central New York enjoy some Finger Lakes wine. Ithaca (ITH) Penn Yan (PEO) or Canandaigua (IUA) are reasonable stops in this region.
Sounds like fun! If I can get my plane out of annual, I'm heading south to the Carolinas, Georgia, and Florida in May-June to hit some minor league parks and visit friends. You can go a long way in a day even at 120 kt (AA-5).