The last two times leaving from New York, we get onto the ship for around 1 PM, we drop of our bags and go and have lunch in the main dinning room, when done with that, the room is generally ready.....
"If your number one goal is to make sure that everyone likes and approves of you, then you risk sacrificing your uniqueness and, therefore, your excellence."
11:00 a.m. is a good time to arrive, it will take approximately an hour to get thru the boarding process and on the ship. You'll be eating lunch by 12:00-12:30, then relax, explore the ship before it gets crowded.
Arriving around 11 is a good idea. You'll be eating in the Windjammer by noon, in all likelihood. (Just remember to complete the online checkin to speed things up.) True, your cabin won't be available until after 1 p.m. or so, and you'll have to bring your carry-ons to lunch, but it still gives you the benefit of being on the ship nearly all day and you'll have plenty of time to explore. Then, when your cabin is ready, you can just drop off your bags!