Philadelphia and Tampa are about 928 miles apart by road. Split the difference and you arrive near Raleigh, the city closest to the halfway point between them. That puts roughly 7 hr 14 min of driving on the Philadelphia side and 12 hr 16 min on the Tampa side — the fairest single meeting point among the cities near the middle.
Over this distance most people will fly rather than drive the whole way. Raleigh still makes a fair, central place for Philadelphia and Tampa to converge, splitting the travel instead of asking one side to cross the country.
If Raleigh doesn't have what you're after, Charlotte and Richmond are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Philadelphia and Tampa.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.