Don't miss the Parade down the Promenade late on the first night - if you get a place outside the pub you will have the best view.
Do not miss the Ice show, you have to get (free) tickets, which they will announce when to pick them up.
Do not miss the Quest game. It's a funny adult game.
Favorite bar? every RCCL ship I go on, we head to Boleros bar, if you like salsa and a lively crowd. YouTube - Liberty of the seas 3 (day1, 2 cruising)
The pub on the Promenade also has a guitar player that is really good, it turns into a singalong every night. Most singles would head for the nightclub late night though..