Two suggestions... Acadia National Park in Maine - Fantastic "bike" paths, called "carriage roads", you can spend days riding. Hiking, mild to strenuous climbing, views around every corner. Bar Harbor is in Acadia, if you want to do the tourist thing there.
Fort Ticonderoga at the north end of Lake George in New York State. Excellent historical site - colonial fort, one of the oldest (if not oldest?) forts in existence in the continental USA. Worth the visit if you are at all interested in colonial history.
