My husband and I went on Royal Caribbean for our honeymoon to the Eastern Caribbean. We got a room with a balcony on deck 6 right near the middle of the boat lengthwise. This is supposedly the best location on the boat to avoid seasickness. The balcony cost us a bundle more and it wasn't 100% private. There were only privacy screens which didn't go all the way from floor to ceiling and neighbors only seemed to go out there to smoke. Yuk! If we go again, we'll get a room with a small round window or an interior room.
Royal Caribbean is very good! Their food is excellent and you have to go to the formal dinners whether you like to "dress up" or not to get the meals of your life.
The food is top notch and so is the wait staff. They really rip you off if you buy alcohol, so don't be all shocked when you get your bill at the end of the week or avoid it totally. There are free beverages to be found.
Get involved and do lots of activities. My husband and I got up at 7 am each morning to make each day feel like two (hey, we wanted our money's worth!) and you have to buy excursions for your port stops. Otherwise you won't see any part of the islands you're visiting.
Say your newlyweds to everyone and you'll get great surprises and an invite to the newlywed party. Also, we went out in the first week of May which was excellent for us: it was after "Spring Break" but before school got out, so we avoided all those rambuncious kids. We wanted a nice "adult" vacation.
Oh, and the best time to enjoy the pool or the hot tubs is when half the boat's at dinner. We got the later dinner and so we enjoyed ourselves in the hot tub during early dinner before we got dressed.
Find out how your cruise line works (like meal schedules and what costs extra as well as onboard and off board activities) and plan your week well. You'll end up remembering a lot more because you were actively involved in planning your activities instead of drifting along from one moment to the next.
Good luck! And buy early to save $$! We booked in January (I think) for a May 1 cruise and it cost us about $2k for: two round-trip airfares, 6 days, 7 night cruise, 3 excursion adventures, all food and drink (no alcohol or pop), and transportation from airport to the docks.