My thought is that the weather in the US in March is anybody's guess. Could be sunny and springlike up North, could be 2 feet of snow, or ice storms
as far south as Georgia. You might have to have alternate plans depending on weather. In other words, come to Miami, and maybe spend more time in
Florida/Georgia if the weather up North is questionable. If weather looks good, then have a plan to take you up toward the Smokey Mountains, etc.
You mentioned Tampa, which is more gulf coast Florida. So why not consider taking 75 West near Everglades, and taking the west coast up, poking around
the touristy towns along the way up toward Tampa. To me, Tampa is just a city, I don't find much special to see there. But I like outdoors, natural
scenery, smaller towns, history rather than nightlife and big buildings
After Tampa, you could cut back over to the East coast of Florida. Again, not sure what is in Jacksonville itself. I wouldn't go there, just pass
Savannah, I've never been, but sounds lovely, and Charleston.
Washington DC, it's great to see the monuments and museums. Baltimore, okay not sure what you'd want to see there, I'd drive on. I think Philadelphia
is a much more interesting city from a visitor/tourist perspective.
You can order online materials from each of the states' tourist boards. Yes, you can see it all online, but sometimes it's fun to get maps and
brochures in the mail and browse through them at you leisure over a cup of tea/coffee or pint.
If it were my trip, I'd stay south if weather is bad, and if weather looks good, I'd want to see the Smokey Mountains (around Asheville, North
Carolina) myself. I've never been there and it's on my dream travel list.
But mountains in snow and ice would not be fun driving or sightseeing.
Also, in the South, you have to consider "spring break" and that tons of students will be partying and taking up a lot of motel rooms, especially at
beach towns in parts of Florida. And families traveling with kids during their spring break from school.