If you only have 60 days, I'd consider taking a train or bus across the center of the country. The center of the country has its own special charm, and I'd hate to see you miss it, but I'd hate more to see you miss other areas.
In the U.S., National Parks are very special places and it's worthwhile going out of your way to visit them. They do attract a lot of visitors, however, so it won't be much of a wilderness experience. Nevertheless, I'd make a special effort to go there.
Stay out of all big cities. Big cities have a lot to offer, but I don't think a bicycle tour is the right time to take advantages of them.
Well-known places are well known because they are popular with most people. Little-known places have a charm of their own, but appeal to fewer people. For example, would you like to see the world's largest ball of twine? Would you go out of your way to see a replica of Stonehenge made out of Styrofoam? Many people would say no to these, but some people would say yes. It's hard to recommend little-known places because we don't know what kind of things you'd be interested in. Sometimes a little-known gem is just a lonely country road shrouded by trees. These places often don't even have a name.