Steel City - can't help you on Princess, as I've never been on that line. However, daytime will be casual - shorts, tees, polos (whatever is play clothes for you), swim suit for pool or ocean, any touring - be respectful of the place you will be visiting. Dinner in the dining room will be either resort casual (think Docker/khaki type slacks and polo/casual button down)or formal (for my husband, this means a tie with his sport coat and dark slacks)suit or tux is appropriat. Shorts should never be worn in the dining room for dinner... are fine for buffet line. As always, discretion is always the better part of valor - if you wouldn't wear it in front of your 10 year old, it's probably not appropriate onboard.