San Diego is the area I always recommend in the US and I've travelled to all 50 states.

Balboa Park (which has the zoo in it and a load of museums), there's Seaworld (though it's a bit over hyped), Legoland, The Midway aircraft carrier, Hotel Del Coronado (don't stay in it but it's worth visiting), Old Town San Diego (wild west themed)

You can take the train down from LA though it's unreliable or United fly there from LAX. You could also look to get a flight to SNA (John Wayne Airport) - AA fly from JFK there on a Flagship service (e.g their good business class) and it's close to both Disneyland and the rail line down to San Diego is a lot closer and easier to access than from LAX. No lounge though, but it's a pleasant airport.