Jersey shore with a trip to Great adventure for your list of requirements.

But for a different kind of fun, definitely try boston. Or NH Coast/Maine. What about Chicago for a long weekend?

Honestly, based on your family's prefs (beach, amusement parks, lively activities), I would go someplace like Ocean City or Rehobeth, and save your money for your bigger trip next summer. Those are perfectly lovely and fun places to visit in the summer, but you can do them relatively inexpensively and so your family could have a great trip with many of the things you all like to do, while not breaking the bank.

NYC combined with a NJ beach? I think Wildwood has amusement parks. 3 days in each would be a nice split and that is an easy drive.

Martha's Vineyard. Big summer destination for black families. Lots to do but you have to like water.

I can't imagine heading to FL in the summer. HOT.

New Orleans, Gulf Shores
NYC
Chicago
Personally I'm dying to do a Yosemite, Grand Canyon, Mt. Rushmore type trip with my older kids.

Would any part of New England work? I'm white, and know many blacks do not feel um ... welcomed in Boston to put it mildly, but what about New Hampshire, the Vineyard, the Cape?

OP,
Dollywood is tons of fun for the kids. Honestly, I cannot address the color issue, but the park has a bird sanctuary, train and tons of really cool rides.

vermont i think great in summer though not a tonne of blacks if that's important.

Myrtle Beach, Jersey shore, Wisconsin dells, smoky mountains

What about the Greenbriar? It's got a lot of different activities for everyone and has a relaxing atmosphere. Plus, it's closer than FL.

Family trips, to date, have been to Disneyworld and more local places (Williamsburg).

This summer I'm looking for a new place. Florida is my fall back, but I feel kind of guilty that our longer vacations have all been in Florida! Planning a Northern-Southern CA trip, but that will be pricier and won't happen until next summer. Would love ideas for places to go. A few stipulations:

-US destination
-More interested in activities (amusement parks, ziplining, beaches, carnivals). My children just never took to appreciating museums (unless it's something quirky) and nature (unless there's an opportunity to see animals).
-Would prefer as diverse an area as possible. We're black so going someplace where we will stick out is to be avoided.
-Will fly, but would prefer a driving location. Will drive up to 24 hours and we can make a sightseeing road trip out of it.
-Need to find a location that will please all of our children (6,12,15,19)

I know that FL has ALL of the things on my wishlist and we've never actually done a non-Disney Florida trip but I would love to expose my children to another area of the country.

Thanks in advance for any ideas!