I do Boston, MA to Palm Beach FL in 2 days (about 11-12 hours each day) . . . If I have old people (75+) with me, it takes longer because they can't ride in the car as long and are more fussy about where they eat meals, etc. Just went there at the beginning of this month . . . then flew out to CA and then back to MA.
For driving to So FL . . .
I-95 is pretty much it. From LI Get on I-95 south -> NJ tpke -> merges back to I-95. I usually do 895 around Baltimore, but it has been under construction, so maybe 695 or just keep on 95 would be better. The GPS may want to take you down 295 after Baltimore towards Washington, but I don't think it is worth it, so stay on 95. At Washington DC, you'll want to follow 95/495, which goes around the eastern side of the city (not Tysons Corner). After that it is pretty much I-95 the whole way south. There are a few speed traps in the NC - SC - GA area, so be aware when the speed limit drops from 70 to 60 (or 55) for no apparent reason.
Figure that you are going to loose about 1 hour due to traffic in the MD - Wash. DC - VA area because there is a lot of construction and often some crashes in those states.
Can't help you with places to stop off for a few days, as we go right through, stopping only at Benson, NC (I think) for the night. There is a Hampton Inn and a Dog Park there (if you are bringing critters) . . . but no place to eat except fast food
. We usually pack a cooler of food and adult beverages for when we stop.