I have taken an Everglades tour which ended at MIA. It was also possible to book it ending in Fort Lauderdale. If you've not been to the Everglades, it's a very interesting tour, and our guide was simply superb. However, you can also have good luck or bad luck when it comes to guides, of course.
We had the same situation when we cruised in July. Our flight was at 5:30 and I didn't know what we could do and more importantly how to get around with all of our luggage (family of 5). So I decided to book a room at the Residence Inn and just relax. It worked out great. There was a great Seafood restaurant within walking distance where we had a nice lunch and then we napped and hung out by the pool the rest of the day. Their shuttle then took us to the airport. It worked out well.
Several times my wife and I have been on late flights coming out of Ft. Lauderdale. We usually rent a car--most of the agencies have shuttles which will pick you up at the pier and drop you at the airport when you return your rental car. This allows us to get around the Ft. Lauderdale area.
One place my wife loves to go is the Sawgrass Mills Outlet mall. It is a huge mall and the shopping ranges from OK to great.