Ft. Lauderdale was our home for 25 years, so I hopefully have some useful information for you.
Day sailing out of Ft. Lauderdale is less than ideal, mostly because there is nowhere to go. If you just want to take the
boat out with no
destination, it doesn't matter if you go north or south; it just depends on the
wind direction. You can even go out to the edge of the gulfstream (you'll know you're there by the change in
water color and depth), turn south, and sail for hours without going anywhere, because the stream will be pushing you north although you are sailing south. Otherwise, plan for the weekend and sail down to Biscayne Bay for a very enjoyable couple of days.