This should definitely be a cross-country adventure! (Actually, I think a road trip would make a cool episode)
Start in NYC–see the sights (Empire State Building; 5th Avenue; Central Park; Broadway show). But NOT the Statue of Liberty (for obvious reasons).
Set off in a car (or the TARDIS) and make westward tracks.
Chicago–Stop off to see the sights and sample some deep dish pizza.
Follow Route 66 through the mid-Atlantic states. Maybe stop off at Graceland to see if Elvis really is dead. Frolic around New Orleans.
Make stops at Mt. Rushmore, Grand Canyon, Las Vegas. See the western prairies and the table lands and dip their toes in the Pacific.
Finally crash at the hotel in San Diego for a little shut-eye before donning cosplays, grabbing tickets, and heading to the convention.