We live in North Jersey, up by NYC, so 2 hours north of you. The Delaware Mem. Bridge has never been a problem for us, somtimes there is construction right after the bridge, but it's never been an issue. Your GPS should just tell you to head south on 95 until you hang a right at I4 in Florida.

Kidding aside, there are only 2 times that you vary from heading south on 95, going around DC and going around Richmond. We go around DC on the Beltway, but always ignore the hint to go around Richmond and go straight through-have never hit traffic(this is always the weekend though).
It will probably be around 14 hours for you to get to FL, so in time for dinner.
We've stopped in Brunswick, GA, which is about 40 miles from the FL border-lots of places to choose from there.
I haven't stayed in FL, so no advice there, but I would buy the I95 Exit Information Guide(or a similar one like this one, which I have this year:
http://www.amazon.com/Drive-I-95-Ex..._1_1?ie=UTF8&s=books&qid=1271605915&sr=8-1)-I wouldn't travel down 95 without it, it's been a huge help over the years.
Here's the website for the other one I like:
http://www.i95exitguide.com/stopovers/index.php
.
HTH