I'll add to the great tips provided by coach32:
Buy a three-day transportation pass. It will enable you to use Bermuda's extensive bus and ferry services without fumbling for change. To go to the South Shore beaches, take the bus (10 or 11, I think) to Hamilton and transfer to the #7 bus. A nighttime ferry ride is also nice.
A good shore excursion for the first-time visitor to Bermuda is the 5-hour island tour. (I did this on my third trip there, and still found it worthwhile.) Do it earlier in the week, if possible.
Onboard the ship: You'll find the longest wait for the dining rooms between 6:30 and 8:00. If you can, go 6:00 or earlier or 8:15/8:30 or later. The ship was built before NCL implemented its open seating policy. If you go to the buffet for breakfast or lunch and see no seats available, go down one flight to the Royal Observatory Lounge. Most people figure this out by day 2, though, but at least you'll have no problem the first day.
I agree that Le Bistro is well worth the cover charge. I also recommend the Pasta Cafe. No charge, as coach32 mentioned, but reservations needed. Should you run into bad weather at sea, try an apple. It's worked for me. If either Elvy Rose or Jane Powell is performing on board, you MUST go to their shows.
When pulling into Bermuda, be out on Deck. The front of Deck 7 is a good spot, but get there early, actually about an hour before your docking time, at least. Just as you are about to enter the cut, look to the right for a special welcome. Once you enter the cut, go to either side of the ship and look down at the rocks for an amazing sight.
I can go on, obviously. Please let us know if you have any additional questions.