Since you won't be participating in the ressie rush, you have lots of options.
I would definatly go and find your stateroom and get rid of your carryon luggage. Keep your camera with you!!
If you have children age 12 and younger who will be going to the Lab, Club or Flounders, I would recommed geting them signed up as soon as possible. later the lines will be longer. It's really not that big of a deal, but there are a lot of kids to be signed up. If you have a teenager, this is the only time you get to check out Common Grounds and the councilors. I think that at 7pm it becomes off limits to adults for the duration of the cruise.
Go enjoy a nice lunch. Tons of great food.
Then its time to explore the ship. Like someone said, start at the top and work your way down. Someone wiser than me said that the lifts (elevators) are for looks only. They are usually crowed and slow arriving. There is different pictures / art in each stairway, so my family spent a lot of time going up and down stairways looking at them. Take a look in all of the different clubs from ESPN to Off-beat before they get over run with people.
Try to figure out landmarks in the ship to help keep you oriented. It is a big ship with many different levels. Generally speaking "Food" ie. restaurants are mid ship to aft, and "Fun" is to the front mid ship to forward (kids clubs, adult clubs, WD Theater, Studio Sea). At one point I think I figured out that the pattern in the carpet in the hallways where the rooms are pointed to the front and back (color red points aft, blue forward). But I am not entirely sure about that.
Take some time to goto the pools if you like.
About 3:30 everything is shutting down for the MANDITORY emegency drill at 4:00. Be sure to go to your room sometime between 3:30 and 4. If you go earlier you will have a chance to look over the daily navigator and see what activites are planed for later in the day. By 4:00 you should have put on your life jacket (as instructed) and go to your muster location when instructed to. Take your camera, it's a great photo op.
When the emergency drill is over, return your lifejacket to your room (put them under the bed so you have more room in your closet.) Then go up to the sail away party, and enjoy your cruise.