The pickup locations for your excursions will be listed on your tickets if you book through the cruise line. Tickets will be delivered to your stateroom the night before you arrive in port.
You have 1.5 hours during excursions, which should be fine. I have 2 excursions with a 45 minute connection time, so I'm planning on bringing a change of clothes and changing near the tender area at Grand Cayman. According to Dave there are facilities near there to change.
Stingray City I hear is the "don't miss" type of attraction at Grand Cayman, and that's one of my excursions that I plan to do.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)