Aft deck under aqua theatre is a nice place to watch the wake.
You can board early (around 11:30-12, depending on how quickly they get everything clean) and have much of the ship to yourself to explore.
Definitely do not miss the roast beef sandwiches in central park cafe.
Skip seafood shack.
Do not miss the aqua show, ice shows, the quest and comedy shows. I agree with booking asap online.
Sit inside at Johnny Rockets for better service.
Head to Central Park for professional photos on formal nights for shorter waits, or to take your own.
If you do the zip line, bring gym shoes, and get there first thing in the morning or right before they close. Sign all paperwork before cruise and have it with you.