If you're main plan is to cruise
the Bahamas then with 3-4 week time limit I would recommend keeping the boat as far south as possible, maybe even in the northern Keys. That is unless you enjoy the actual sailing part more than the hanging out part.
If you're goal is to spend the max time hanging out in the Bahamas then further north you will spend up to half your 3-4 weeks just preparing and getting to your destination
If you keep the boat in south FL it will take a min of three days to arrive and load food
and water, sail to Freeport
and clear customs
. This assumes you splash the boat and have absolutely nothing to repair or maintain, no fuse or light bulbs to replace, batteries
all charged, etc,
Then once you clear in to the Bahamas, from either spot you have about 100 miles more dead upwind to reach the first good cruising grounds, either Abacos in the north or Berrys in the south.
So I would figure a week from the day you arrive until you reach cruising grounds and plan a week to get back and get the boat back on the hard. If you have a three week trip then that leaves about a week for the hanging out part.
This is all if you are based in south Florida. If you are in central or north Florida then add another day or three to the travel time. Plus all this assumes you will have no weather
delays which in the winter can keep you holed up in Florida for days or even weeks.
Not trying to discourage your plan, just want to make sure you understand what's involved.