Having done both Eastern and Western, I recommend the Western itenerary. It feels more "caribbean." I don't really care for Nassau, St. Thomas, or St. Martin. Out of the three, St. Martin is the nicest. The Western itenerary includes Jamaica, Grand Cayman, Cozumel, and Castaway Cay. I find these ports to be more tourist (especially kid) friendly.
Excursions... I don't necessarily recommend doing an excursion at every port. That adds up fast (not to mention you have to get up and off the ship early for most excursions).
For Jamaica, I highly recommend Mystic Mountain, a brand new tourist location with Jamaican Bobsled (rollercoaster-like ride), zip-line (the best zip-line course I've seen in the caribbean), a pool with a slide (this is included with all excursions), a scenic 15-minute chair lift (total of 30 minutes roundtrip... you can purchase this alone, but it is a better deal to purchase either bobsledding or zip-lining), and a restaurant (but it's better just to eat on the ship where you won't have to pay extra). The staff is very friendly and professional. We were very impressed. The excursion was well worth the money. I also hear that the falls are wonderful (but you need tennis shoes for this). I recommend booking an excursion here because in Jamaica, you really don't want to get off the beaten path. Only shop in locations your ship recommends, and don't take a cab (they'll probably tell you this several times).
For Grand Cayman, I would recommend some tour that takes you by millionaire row and ****. There's also a lot of shopping in Grand Cayman. This is a port where you don't need an excursion.
And Cozumel... beware of run-down "luxury" resorts, where most excursions take you. Cozumel was hit by a storm a few years ago, and is still recovering. I've done the Zip Line Adventure park... we were expecting a zip-line through the jungle... no, it was a zip-line between rock walls. It was a lot of fun, though. It also includes snorkling... I'm not a fan of snorkling. There weren't many fish here... or even pretty coral. The guides toss out food to get them to swim up to you. You're also welcome to stay at the resort as long as you want, and you get one free drink (do not get anything over ice... they'll warn you this about this, as well). They have a pool, but it was FREEZING. The existing part of the resort was actually pretty nice. We've also done a clear kayak adventure at another resort... that was more of a disappointment. On the brochure, they had a picture of two lovely wicker chairs... which were the only two wicker chairs at the entire resort!
Yes... their beach chairs were luxuriously plastic. The beach was not a beach, but a bunch of rocks. It was overcrowded and our tour kept getting delayed. The equipment was actually in good shape, though. The kayaks were really clear, and we saw a lot of fish (though they were lured by food that the guide would hide and pretend not to have... our guide was a moron). There was also snorkling... but we had to walk a mile to get to it, then walk a mile back. Our moron guide swam fast and left a few of us behind. Like at the other resort, you could stay as long as you wanted, but we wanted to get the heck out of there (we also had drink vouchers... and got extras when we complained about our wait times... and there was fruit. I was a little worried, but I ended up eating an apple because I was hungry). The pool there was also freezing (not to mention dirty).
If you're leaning towards Eastern, I can give you some more details about those ports, but for right now I'm just going to say
do not do snuba in St. Thomas.
Also... if you're hoping for some dolphin interaction, I actually recommend not booking this with the ship (and do not do in Nassau). Most dolphin encounters include sitting in 4' water while dolphins swim up to you. You'll want to really do some online research to make sure you get the dolphin experience you're hoping for. I sat in a hot tub with a father who booked his family's dolphin encounter in Jamaica online, and he was very pleased with himself (they got to actually swim with the dolphins). These dolphin excursions are very pricey, so you'll want to be sure you get what you want.