The 2nd one is more interesting because of Merida

Dont expect much on Belize City - unless you take excursions (on your own or join the ship's), you would not find anything worthwhile at Belize City.

3 day at sea? there is one sea day one port day followed by another sea day... that is a perfect set-up.

Only those who have not cruised before, would think sea days are boring - if you are on a new ship, you would find yourself have NOT ENOUGH time to enjoy the facilities the ship can offer. But if you take an old ship, then tough.

Out from Galveston I think the best choice would be Grand Princess. This might be the last year Princess will sail out of Galveston.

Search Yucatan Peninsula of Mexico you will find more than enough information for your Mexican Ports.

The only caution I would offer is, these are popular ports and you will find there are 7 to 8 ships visiting same port on the same day. It could be a big problem for Grand Cayman as it is a tendered port.