I can't sleep past 5:30 am so I usually have the boat alone to myself for a solid 3.5 hours before mayhem ensues. I get all the good, freshly cut fruit and whatever fresh preparations they have available at cabanas; best part is you can have a nice, quiet, solitude breakfast watching the sun come up over what seems like endless water. It's also a time for a good swim in the pool once you can as you'll be one of two people in it and there will be no splashing kids. Then 9 am comes around and everyone including my wife has to come up on deck ruining everything.
Ultimately, when I'm at port I LOVE to see new places. I can always have a quiet ship if I try hard enough, I probably won't ever get to Nassau again (I'm only doing a 4-nighter due to work constraints, i'd be on a 7-night Caribbean if it was my choice)...