Well the first thing that came to my mind was St. Louis, Mo. I live about 30 or so plus miles fwest of there and we have some amazing free things. While some "extras" might cost the admission to the St. louis Zoo, History Musuem, Art Musuem, Forest Park (larger then Central Park and its where all the above are located) are all FREE! You can walk the park to get to these. Forest Park is within walking distance of some hotels as well.
Good Luck on your adventure!!