The fair place to meet is Raleigh-Durham, NC — the city closest to the midpoint of New York and Tampa. From the farther side that’s about 12 hr 16 min of driving.
Recommended midpoint
Raleigh-Durham, NC
From New York
8 hr 53 min
423 mi to Raleigh
From Tampa
12 hr 16 min
585 mi to Raleigh
New York has the shorter trip; the split is off by about 3 hr 23 min. The alternatives below can even it out. New York and Tampa are about 1,004 miles apart.
New York and Tampa are about 1,004 miles apart by road. Split the difference and you arrive near Raleigh, the city closest to the halfway point between them. That puts roughly 8 hr 53 min of driving on the New York 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 New York 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 New York and Tampa.
Raleigh is the capital city of the U.S. state of North Carolina. It is the second-most populous city in the state, tenth most populous city in the Southeast, the largest city in the Research Triangle area, and the 39th-most populous city in the U.S. Read more →
New York, often called New York City (NYC), is the most populous city in the United States. It is located at the southern tip of New York State on New York Harbor, one of the world's largest natural harbors. Read more →
Tampa is a major city on the Gulf Coast of the U.S. state of Florida and the county seat of Hillsborough County. Tampa's borders include the north shore of Tampa Bay and the east shore of Old Tampa Bay. Read more →
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.
Estimates use straight-line distance and typical road speeds; real drive times vary with route and traffic.