According to Kettlewell, the distance from Palm Beach to Charleston via the ICW
is 369 miles. If you want to travel full days, you should have nearly 10 hours of good daylight for traveling in the summer. So figure what your average cruising speed is per hour, multiplied by the number of hours per day you want to travel, and divide that into 369 to get the number of days it will take. I would also add a bit of time to that for bridges, sightseeing (especially if you have never done the trip before), etc.
If I were you, I would take the outside route
at least to Jacksonville
to avoid all the bridges in Florida
. It would even be worth waiting for a weather
window to do it. Last year, we went from Ft. Lauderdale to Charleston on the outside in 2 1/2 days, and it was delightful.
There's a lot to see along the way, so if you choose the ICW, I would allow lots of time to visit St. Augustine, Cumberland Island, Jekyll Island, Savannah, etc. Just my two cents.