My partner and I took our first cruise last year, and we chose the Century out of Miami. I'll start with the good stuff, and then finish with one minor critique.
1) Good stuff:
We loved the ship. Indoor spaces reflect a classy elegance without being stuffy, and without the gaudy showiness that I've seen pictures of from other cruise lines. My partner spent a good bit of time relaxing in the library, watching the waves roll by and reading a book. We both particularly enjoyed the martini lounge - perhaps too much! The main dining room is absolutely gorgeous, and the food is well above average. We did the anytime dining option, and there was never a problem seating us when we wanted to eat. The buffet off the pool deck (whose name escapes me at the moment) always had tasty stuff on offer, with great big windows that showed off the beautiful blue Caribbean. The theater was nice, although the entertainment choices were limited. There was a funny comedian one night, and we had a great time with that.
Outside spaces: The bar directly outside of the buffet area at the back of the ship was a lovely spot to grab a margarita and gab with your new friends. The pool deck could get a little crowded, but I never had a problem finding a spot to enjoy a little sun and a good book.
The staff was generally very friendly and helpful - waiters were prompt and attentive, bartenders mixed killer drinks - especially at the martini bar - and the customer service desk was on top of things.
We had an inside cabin, which was tiny, and waking up in the dark wasn't my favorite thing in the world. Still, the cabin was very well-appointed, the bed was comfortable, and the bathroom was adequate. That's all we really needed.
Our cruise was unexpectedly diverted from Grand Cayman to Key West because of high seas or something. Celebrity really surprised me with how quickly they put everything together - within two hours of being diverted, they had new shore excursions, and everything was totally organized to get us to Key West. We had a fantastic time there - we rented bikes and went to this butterfly sanctuary that was just entrancing. I give Celebrity a lot of praise for how well they handled that diversion.
Oh, if you cruise to Ocho Rios, and you feel you must get off the ship, DO AN EXCURSION. Do NOT, I repeat, DO NOT try to go into town on your own. You will get annoyed to death by unscrupulous cab drivers and other people who want to rip you off. Ocho Rios is an unpleasant little place, and if I were you, I'd just stay on the ship.
2) Ok, the bad stuff:
The pool deck closed at dark. I'm not sure why, but ship activities really seemed to wind down in the evenings. Sure, there were the shows, and the bars, and the casino, but would it have killed Celebrity to have stuff on the pool deck at night? I keep seeing pictures of Princess ships showing outdoor movies on the pool deck at night. That sounds really cool.
Honestly, though - that (and the awful dump that is Ocho Rios) was really our only complaint about the cruise. We really had a fabulous time. We're seriously considering booking another cruise for November on the Eclipse.