Don't listen to the negative reviews, complaining about the ship's age and the staff. After a week on the Celebrity Infinity, I'm convinced those reviews were left by picky and miserable people. Yes, the ship is definitely old, but it's very clean and well-maintained. And I can't even begin to tell you how incredibly the staff was. We've previously sailed with Princess (just okay) and NCL (horrible experience). My husband and I agreed that we'll look at Celebrity first, for all future cruises.
We booked a Concierge Class stateroom, and never regretted it. Our embarkation time was 11:30. We arrive about 5 minutes early, and were on the ship with a glass of champagne in hand before 11:45. I still can't believe how smooth the check-in process was. We spent the next couple hours enjoying the pool bar while waiting for access to our rooms. The stateroom was outdated, but very clean. Our Concierge, Jonathan, was fantastic. He provided guidance with a couple ports, and was able to quickly re-schedule our disembarkation time to accommodate the transfer we booked outside the cruise line.
The food in the main dining room was overall amazing (we each had only one meal that was not so great). The service team (waiter, assistant waiter, and sommelier) were very friendly and attentive. The buffet was always clean, and the food was much better than expected. We took part in a Wine and Food pairing, and the host, Fernando, was absolutely hilarious!
The Concierge Class offer extra perks: Concierge available in the library each day, canapes delivered to the room each afternoon, tote bag for shore use, and better toiletries. The beds were comfortable, and there is an exclusive pillow menu for this class.
Booked private hotel transfer through GetYourGuide, which was better than any transfer options provided by the cruise line.