The fair place to meet is Charlotte, NC — the city closest to the midpoint of Raleigh and Tampa. From the farther side that’s about 10 hr 44 min of driving.
Recommended midpoint
Charlotte, NC
From Raleigh
3 hr 15 min
130 mi to Charlotte
From Tampa
10 hr 44 min
512 mi to Charlotte
Raleigh has the shorter trip; the split is off by about 7 hr 29 min. The alternatives below can even it out. Raleigh and Tampa are about 585 miles apart.
Raleigh and Tampa are about 585 miles apart by road. Split the difference and you arrive near Charlotte, the city closest to the halfway point between them. That puts roughly 3 hr 15 min of driving on the Raleigh side and 10 hr 44 min on the Tampa side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Charlotte suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Charlotte doesn't have what you're after, Orlando and Atlanta are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Raleigh and Tampa.
Charlotte is the most populous city in the U.S. state of North Carolina. With a population of 874,579 at the 2020 census, it is the 14th-most populous city in the U.S., seventh-most populous city in the South, and second-most populous city in the Southeast. Read more →
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 →
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.