Weather permitting, I'd head out at Lauderdale and do an overnight hop up to Ft Pierce. Won't have to leave real early, as I usually make that run from Miami. Inside, it's a day to Lake Worth, and then a day to Ft Pierce. I stay at Harborgate in Ft Pierce when I take a slip instead of anchor.
From Ft Pierce you can do an overnight outside to St Augustine, or 3 days on the ICW. From there it's a days run up to Jacksonville or on past to Fernadina Beach (not sure if you can reach St Marys in a day). Then a couple of short days to St Simons (I stopped at the north end of Cumberland Island). I usually go outside from St Augustine to the North end of Hilton Head Island, but you could go to Savannah instead.
A day to Beaufort, SC, then 2 days to Charleston, as I recall. Two more days to Georgetown. Or go outside at Charleston for an overnight to Georgetown. Strong outflow when the tides running out.
Georgetown to Myrtle Beach is to me, the prettiest part of the ICW. Though through Myrtle Beach is the ugliest. From Georgetown, you either push hard, or take short days. Or go outside. There's a marina to your right just before the bridge at Wrightsville Beach. Last time I was there they had a free 1 hour loaner car. I would go outside from Wrightsville Beach to Beaufort Inlet. If the weathers mild, you might want to spend a night in the Cape Lookout Bight. Inside, it's a two day trip to Beaufort/Morehead City. Lots of skinny water on the second day. If you stay at the Bight, take a short day and stop at Beaufort.
I'd stay inside up to the Chesapeake. Lots of open water for sailing, and lots of destinations. Days run up to Oriental, then it's pick and choose to head north or make some side trips. Dismal Swamps a prettier run over the Virginia Cut. If you take the Cut, you can make Newport in a day from Coinjock. From Newport, I'll let the folks on the Chessie add their input.
Almost forgot, while you're in Lauderdale pick up Skipper Bob's guides for the ICW, and if you have internet on the trip http://cruisersnet.net/
is a great ICW resource.