The National Park Service, a part of the United States Department of the Interior, maintains some 400 or so units across this rather sizable Republic. This blogger has very much enjoyed visiting these parks, battlefields, and monuments, from the Everglades and Mount Rainier, to Gettysburg and Shiloh.
For more on the National Park Service, in general, you might note their webpage, and see what is in your area, if you are in the states: http://www.nps.gov/
A page out of my book.
Recently, I had the opportunity to note and discover the "Passport to your National Parks" booklet that can be found in most National Park gift shops. Of course, the books is designed to encourage you to collect stamps -- both those similar to postage stamps, and cancellation ink stamps like those given at a customs station on a border. The likeness of page 33 in my book gives you an example of both.
You can find the books and stamps sold on this page:
This link provides a list of which parks were featured in the adhesive stamps for each of the years:
This site presents an impressive personal collection that gives one an excellent idea of how many stamps there are out there (Manassas Battlefield, for instance, has at least 4 if you visit the various buildings!):
Finally, these folks have made collecting the stamps a kind of treasure hunt:
Waymarking.com: NPS Passport Cancellation Stations, A-Z
Often a park will have but one or two stamps. A few locations -- especially in the Washington, DC area -- will reward you with a massive number in one place. For my own part, I might note that the headquarters of the George Washington Memorial Parkway, located in Turkey Run Park, in McLean, Virginia, has 34 stamps, including the Parkway itself, but also Great Falls, Roosevelt Island, the Arlington House, and the USMC War Memorial. The bookstore at the Washington Monument has stamps for all of the major monuments on the Mall, along with Ford's Theatre and Pennsylvania Ave NHS.
The next time you are in a NPS visitor center, you might ask about the stamps...
I found this one on line, and need to find the time to get up there for my own: