I have made the drive there (at least from Atlanta) so many times that I lost count.
If you have some time, break it down a bit and it's not horrible at all.
Personally, I always enjoyed kinda leaving earlyish and getting to either the St Pete or Clearwater areas. Have a nice dinner and evening out. Some nice hotels around. Hang out until check out time after having a nice breakfast. Maybe take a walk around a bit depending on the weather.
Hit the road and roll into Miami early evening--ish. At that point, get the party started.