Here are a few places I think are worth visiting. Not in order, just as I though of them.
Nature and Natural formations.
Yellowstone and Grand Tetons
Glacier National Park
Mt Rainier Nat. Park
The Olympic Peninsula
Jedediah State Park and Del Norte Coast Redwood State Park (Crescent City, CA)
Sequoia National Park/Kings Canyon
Death Valley
Zion National Park/Canyon Lands/Grand Canyon (Utah)
Petrified National Forest (Arizona)
Algodones Sand Dunes
Colorado and North New Mexico (National Forest areas)
Everglades
Great Smokey Mountains National Park
Acadia National Park
These are some populated areas that I feel offer something unique.
Town/Cities
New York
San Francisco/Bay Area
Seattle
Chicago
Boston
San Diego/LA
New Orleans
Austin, TX
Gulfport, MS
FL Keys
Charleston, SC
Savannah, GA
Orlando, FL
Annapolis, MD
Newport, RI
Cape Cod, MA (not a "town" but thought it fit here)
Nantucket, MA
Portland, ME
Burlington, VT
Napa/Sonoma, CA
Colorado mountain towns (Steamboat Springs, Aspen, Durango, Olathe, Glenwood Springs, Vail... etc)
New Mexico mountain towns (Taos, Los Alamos... etc)
Traverse City, MI
Mackinac Island, MI
Ashville, NC
Ashland, OR
Santa Cruz, CA
Puerto Rico
US Virgin Islands
and of course more...
Specific touristy things, but worth seeing..
Georgia Aquarium (Atlanta)
National Art Gallery (DC)
Museums in DC and NYC (Smithsonian/MET/american nat. history)
Niagara Falls
My personal recommendations.
What may or may not qualify as off the beaten path.
Mayville, NY (Lake Chautauqua and the Chautauqua Institute)
Crescent City, CA (Have been twice, and will go again, amazing place.)
Land of Lakes area of Wisconsin.
Intercourse, PA (Amish country, interesting area, next to Blue Ball, PA)
Fernandina Beach, FL (great beach)
Some aren't near water, or beaches... But everyone of the listed has something unique and interesting to offer.