There's Montezuma Castle in Las Vegas,NM where United World College is located. Students from all over the world come here to study.
Around Tilton, NH (between Cocord and Laconia) there is a Shaker Village. They give tours and the structures are still in their original condition. It's beautiful rolling countryside. It's also home to one of the major car races every year.
In Laconia which is quaint in its own way is home to Lake Winnepausagee (? sp). You can take rides on the postal boats for a 45-60 minute cruise, see all the old summer "cottages" (mansions) that are passed down from generation to generation. You can also see the cottages on the islands in the lake.
In NY State you have the beautiful Adirondack Mountains. Lake Placid is there and that's where the 1970's (I think that was the right decade) Winter Olympic Olympics were held. Nearby is Dannemorea State Prison.
Also in NY you have the Thousand Islands on the St. Lawrence River separating the U.S. and Canada. You can stand on the banks and watch the ocean-going vessels pass through. Sometimes the ships get backed and the sailors will start conversations with you--if you can understand them. Eventually they move up to Messina, NY, where they go through the locks to reach the Atlantic Ocean.
Atchison, KS is a small quaint town that was the home to Amelia Earhart. It's been turned into a museum. It's also the home to Benedictine College and a Benedictine Abbey that's gorgeous.