From the May 24, 2014, Parade Magazine "The Most Popular Tourist Attractions in All 50 States, According to Trip Advisor" by Vi-an Nguyen.
Trip Advisor used their "Trip Advisor Popularity Index" including quality, quantity and recency of reviews. Some spots that you'd expect to make the list, didn't make it like Disneyland or the Statue of Liberty.
ALABAMA-- USS Alabama, Mobile
ALASKA-- Anan Wildlife Observatory, Wrangell
ARIZONA-- Red Rock Scenic Byway
ARKANSAS-- William Clinton Presidential Library, Little Rock
CALIFORNIA-- Pacific Coast Highway, Route 1, Los Angeles to Carmel.
COLORADO-- Trail Ridge Road, Estes Park
CONNECTICUT-- Philip Johnson Glass House, New Canaan
WASHINGTON D.C.-- Lincoln Memorial/Reflecting Pond
FLORIDA-- Stetson Mansion, DeLand
GEORGIA-- Mickve Israel Temple, Savannah