If this is a first time visit to the area, my advice would be to travel around spending time in several places. We flew into Boston, drove up into Maine, traveled west into New Hampshire and then finally into Vermont and back to Boston. We thoroughly enjoyed making this loop and not being stuck to one locale. There are so many unexpected twists and turns if you have the freedom to meander and not be tied too long to one place.
Vermont is good but is not really central to New England. However, if you are considering upstate New York in your plans then you are pretty close. I consider the Mt. Washington Valley area (Jackson/Conway) of New Hampshire as central as you can get for New England proper if there is such. From that area, you approximately three hours from Boston to the southeast, Camden Maine to the east, Canadian Border to the north and Lake Champlain (VT and NY border) to the west.
This area is awsome in itself including the Kancamagus Highway, one of the most scenic drives in New England for fall foliage. There are some excellent historic inns and B&B's in the area. If you enjoy tax free shopping, Conway is known for that. Mt. Washington is the highest point east of the Mississippi if you like mountain drives.
I hope this helps.