Just got back from this cruise (7/13 - 7/20). My wife and I had the best time! (But what do I know - it was my first time on a cruise). However, I have traveled a great deal and it was the best value for the money we have ever spent on a vacation.
To answer your questions:
Jamaica - We did the Dunns River Falls tour and except for climbing the falls - hated it. The bus ride there was too long (almost three hours!) We made one stop at a "rest stop" where the locals offer you their souvenirs or some ganja if you want it. Didn't feel very safe there, some guy came up to my wife and was bothering her the second I went to the rest room. Once at the falls, you climb up the falls with about 1,000 of your "closest friends". It took us over an hour and a half to get to the top. That was worth the experience of doing it once in your life. But not again. Then as someone else stated, the maze of shops at the top don't feel very safe. They harrass you to buy something. One guy actually took me by the arm and dragged me to his stand! (I'm not tiny - 6 ft 2 in. - 225 lbs) I wanted to get out of there right away. We ended up buying something from him we found later at Montego Bay for almost half the price and that was after we haggled with him to drop his original price by half! On the bus ride back, same rest stop, but we didn't even get off the bus that time. Then shopping in Montego Bay for a half hour before we had to get back to the ship. We haggled for our souvenirs, got them dirt cheap and they fell apart once we got home. There has got to be a better excursion, just be safe and keep your eyes open and on your family.
Grand Cayman- Much nicer and safer than Jamaica, but much more expensive too. Was looking forward to this port because I once spent two weeks here years ago. Not enough time to do everything I wanted. We took the island tour and Stingray City excursion. No time for shopping afterwards because we had to get back on the ship. But I will tell you no price haggling here, and everything is very expensive! Plus $1.00 Cayman = $1.25 US.
Finally, never having cruised before I cannot compare the Conquest to other ships, but we felt it was beautiful. The staff was friendly and accommodating. We felt the service was great. We ate at one of the two formal dining rooms (Monet) every night and always had a great meal. Don't be afraid to ask for more food, like a second lobster tail, etc. Everyone at our table did. We had a late seating so we didn't have to rush back to the ship on port days. The buffet was good. We would eat there for breakfast and lunch. Everyone recommends going to the Point supper club. It is $25 per person and looks good, but we did not eat there. There is a 24 hour pizzeria, which I would grab every night! See the shows, but avoid the magic show the Deja - not very good. The comedians we saw were all good. Don't play bingo, we felt it was fixed... There was one guy who won twice in the same session and didn't seem to care, like he knew before hand...
If you are going to book your excursions on the ship, do it through your TV. It is much easier than standing in line with 20-30 other people.
Alfred's bar is nice if you like jazz music, cigars and martinis. Vincents bar had a duo from Nashville that played c and w and some pop tunes. The Degas Lounge had a Philippino three piece band that played alot of "light rock", Eagles, Jimmy Buffett, etc. The night we saw them only three other people were there, but they were good. As a matter of fact, for having almost 3,000 guests on board, there never seemed to be alot of people around. (Except when getting on or off at the ports). I guess there is so much to do and the ship is so big, it doesn't seem crowded.
The disco (Henri's) was never very busy on our cruise and there was security there checking ids (You had to be 18 to enter). I think this is because it is right by the teens area. That looked cool. We have an 11 and 15 year old, that we plan to take on this cruise next year and we think they will have a blast. The teen area included a "bar" for drinks, a dance floor, and video arcade games. It was always crowded and the kids all seemed to be having fun.
Overall, we had a excellent time and sure you will too. If there is anything specific you want to know, please feel free to ask.
Mike