We have been on the Connie 3 times, the last being for 2 weeks over Easter of this year in the Caribbean.
We love the ship.
As one other poster mentioned, Connie and all of the other M-class hips have an adults only area which is forward on the pool deck; you can't miss it. In there is our favorite thing, and why we love the M-class ships: the Thalossotherapy Pool, or as we call it, the T-pool.
It is a heated pool, adults only, seawater, that features areas on both sides that have a series of round bars that you can lay one....underneath the bars, the water bubbles and provides a massage like experience...you will love it.
Also in this same area is what is known as the AquaSpa Cafe, and it is behind the T-pool. It features light fare. We always have either the yougurt parfeits or the meusli in the mornings....for lunch the have various light dishes, and I am told you can order broiled (?) salmon any day for lunch. Try it....you'll like it...to steal a line from an ancient Alka-Seltzer commercial....
Our other favorite on this ship in particular is an entertainer called Perry Grant. He is featured nightly in Michael's lounge. I think his show starts at 7:30, but if you are not there by 7:00 or a little after, it's SRO. I won't try to describe his act, but it involves a lot of music - he sings and plays the piano - and some "campy" banter. You will either love him or not care for him Try and get to at least one of his shows. He also has a late shown nightly.
As for specialty restuarants, we have eaten twice at Tuscany, and can't say enough about it - we love it. Also very good is Bistro on Five. We have not done Ocean Liners, but have dined in the equivalents on other M-class ships. truth be told, to us, once was nice, but we prefer the less formal Tuscany. Again, personal choice.
We have opted for the Anytime Dining option, or whatever the name Celebrity has for it. We are early diners, and are usually there either at opening time or soon thereafter. We have had excellent service and have never had to wait for a table for 2.
Another nice venue is the Rendezvous Lounge, just in front of the MDR. It has a comparatively large dance floor, and the music there is nice as well. We particularly enjoy watching the skilled couples dance, and it seems like there are always a one or two couples that are really good.
That's all I can think of for now, but if you have any specific questions, I will try and answer them.
enjoy the voyage !