I’d suggest picking one of the springs with cabins and using it as a base of operations - most of the central springs are within an hour or two’s drive of Williston.
Cabins available: Devil’s Den, Blue Grotto, Vortex.
Camping available: Ginnie, Manatee, Ichetucknee (cavern cert required to dive),
On-site fills: Devil’s Den, Blue Grotto, Ginnie.
There are also some budget options for overnight accommodations - a number of folks on this board have diver rentals in High Springs, Dive Outpost offers cheap accommodations out by Peacock, Cave Adventurers has accommodations out by Jackson Blue, etc.
You also don’t need on-site fills; north central Florida is blessed with many dive shops that will cave fill nitrox (and hell trimix, if you had the certs).
For fills, stop by Extreme Exposure or Cave Country (High Springs ), Bird’s Underwater (Crystal River), Amigo’s (Ft White), Ocala Dive Center (Ocala), Big Guy Scuba (Peacock), etc…this list isn’t comprehensive, there are a lot more great shops out there too.
Amigo’s is worth a stop if you’ve never been there by the way; it’s a self-service fill station open 24/7. You can fill up your tanks anytime of day or night with air, 32%, etc.
In terms of springs, the flooding on the Suwannee has shut down a lot of dive sites; a few are reopening but vis is questionable/not the best. For open water/cavern, your best bets in the near future are the private springs (Ginnie, Devil’s Den, Blue Grotto, Paradise), Jug Hole at Ichetucknee (requires cavern cert), Manatee (Catfish & headspring), Rainbow River, and Buford (although I hear visibility yesterday with the storm rolling in was quite bad). The panhandle springs (Vortex, Morrison) should be okay.
There’s a map of the springs
here.