Regarding the speeding, it doesn't matter how fast you go as long as you blend in with the other traffic. If you are alone, then keep it under 10 mph under the limit and you will be fine.
It's tough not knowing what you are into, but here are some of my favorite spots.
ME: Kittery Trading Post is one of my favorite stores and there is plenty of other outlets that my Ms. and kids can hit so I don't have to rush through the store. Any of the small towns along the coast (follow Rt. 1 North) are cool and if you are lucky you can buy a lobster meal off a boat coming in a one of the many marinas (some will even boil them for you). Freeport is home to LL Bean and has a number of outlets, but isn't as cool as KTP IMHO. Baxter State Park and the Moosehead area are great places to hike and camp. Lots of great areas for whitewater rafting and canoe trips. I love seafood and this is one of the best places to get it fresh.
NH: tax free state, so enjoy. White Mountains for hiking, camping, canoe / white water rafting; Conway is a good place to stay to get the full atmosphere.
VT: Green Mountains for hiking, camping, canoe / white water rafting and mountain biking.