We have never sailed on Princess, but have visited on other lines each of the locations you mention.
Cozumel is, as you probably know, an island separated by a 45 minute ferry from mainland Mexico. The island is pretty but not especially historic. Snorkling is big there and the ships generally dock or tender directly into town or a bit down the road. We have enjoyed going to the mainland to visit Tulum, a breathtakingly beautiful cliff over the ocean Mayan ruin. Staying the island is also great, even if not adventure driven. The town is typical cruise ship shopping. There is a small plaza and shopping center within walking distance that has some nice and unique local artists. Very inexpensive. We agreed to overpay on our last visit as it was Christmas eve and dark and the artist was still there for us. However, overpayment was five small tempra paintings of the coast for $28. We really enjoyed visiting the national park on the island, Chanakanaab, is very pretty. It has great facilities, approximately $10 entry, with restaurants, dolphin encounter, snorkling, beach, etc. But most fun is the helmet diving. You are given a helmet attached to an air hose and walk, yes walk on the bottom to explore about 25 to 30 deep. It is great and you can even wear glasses under the helmet. If you don't want to get wet, try the Atlantis sub. My wife and non-swimming youngest son went and loved the experience.
Costa maya is a pretty make believe place built by and for the cruise ships. Unless you go inland, as you suggest there is only a shopping plaza and small beach. Either relax and shop and eat or take the excursion. The shopping is very unforeign as it is merely cruise ship built stores.
Grand Cayman is a beautiful island. However, the recent hurricanes devastated the island. Tourism is back up and running but the damage is still extensive as they rebuild. Acres and acres of palm trees and gone or bent over and hardly a house or building did not sustain damage. Luckily, the standard of living is pretty high and the economy is bouncing back. On our recent trip over christmas we did the stingray city tour. We heartily recomment Captain Marvin. You go out to the sandbar, approximately 2 or so miles off shore immediately before the breaking reef that surrounds the island. you then anchor and wade, yes wade amoung the stingrays. It is not even in sight of land and you are wading in the ocean. The stingrays are plentiful and harmless. You can feed them, stroke them and even hold them a bit. At first it is unnerving as they are huge sea creatures. When one bumps or brushes you it is quite a scare at first. We liked Captain Marvin's 2 hour tour as it is on a small boat with no more than 15 or 20, in contrast with other boats with far more. I had no interest in doing more snorkling as I simply can't seem to do it and it frankly scares me. The boat does make one more stop to snorkle a reef and many stayed on board. My oldest son snorkled the reef and thought it was great. You are then returned either to a beach or downtown. Also, the Captain Marvin price was less than that of the ship and available on line or by 800 number. the town, Georgetown is filled with shopping. Jewelry stores abound and the Rum cake factory is a great visit to buy real rum cakes or just to sample. Also, if interested in inexpensive local art, the historical society immediately across from the tender dock is a good stop.
Belize - Belize is definitely a developing country. The town you tender to is very depressed and not a place to go wandering around. Even our guide stated that you should not simply walk around, in contrast to Georgetown and Cozumel. We choose an all day tour to ruins in the jungle that were no where as developed as Tulum. Literally, you take a hand cranked ferry across a river and then to the ruins in the middle of the jungle. You are free to climb on and explore ruins that in the US would be off limits because there are no ramps, rails, etc. We even saw the army guards with machine guns to protect the ruins from Guatemalean insurgents. Otherwise, Belize is an eco-tourist place for the adventure driven.
Hope this helps. So you know and can best judge our comments, I am a 48 year old attorney, wife is 48 year old elementary teacher and we have 16 year old HS junior and 19 year old college junior.
Let me know if I can help out.
Hal
Voyager - Christmas 2004
Zaandam - Christmas 2003
Norwegian Sea - Christmas 2002
Monarch - Christmas 2001
Color Festivale - Summer 2001
