Hello Shelia and welcome to the wonderful world of cruising. For your formal nights a nice cocktail dress or dressy pants w/a dressy top,will do you just fine, you will have two formal nights. For a man a nice dark suit or suit separates will be just fine.
There are a lot of hotels to choose from, most have shuttle service to the pier, we stayed at the Holiday Inn West - nice hotel.
As for things to do in Grand Caymen- a snorkel tour to Sting Ray City is a must do, you don't have to snorkel or even know how to swim to totally enjoy those amazing sea creatures. Where in Mexico are you going, you didn't specify. I would be guessing Cozumel? if so, we always book a snorkeling tour thru the ship out to the Palencaar Reef - its amazing, and all you have to know how to do is float in the water, you have a dive master with you at all times, who will teach you the basics of snorkeling and is there in the water with you at all times to help.