My parents are going on a Celebrity cruise in June and I have done a lot of research for them. It sounds like they are a great cruise line but many of their passengers are adults. I was on here researching Celebrity for my mom when I came across your post.
I am 27 but I act like a teenager. : ) I took a cruise on Royal Carribbean's Explorer of the Seas at the end of August and had BLAST! I don't know if you have your heart set on Celebrity, but the Explorer would be the perfect vacation for your teenagers and you and your wife. They have a rock climbing wall, an ice skating rink, a roller blading track, a miniature golf course, basketball, volleyball, ping pong, pool games, tropical parties on the deck in the evening with dancing and dance lessons, a huge arcade, self serve ice cream available around the clock, they have three pools and three hot tubs, they have a spa with workout equipment and classes and they have a ton of activities to participate that would be perfect for teenagers and for adults. They also have a game room with tons of board games. There were a lot of teens & kids on our trip. Just like the other ships, there is a really neat disco that looks like a castle for teens and adults. I do think they kick people under 17 out at a certain time but your kids could go play mini golf after that if they wanted to hang out together. My hubby and I found that a great time to play mini golf was around midnight because a lot of the people went to bed. You can play all night if you want to.
The shows are all great too. The earlier ones are family friendly and the later ones (after 9 p.m.) are not appropriate for some kids. Yours are older though so it's up to the parents to decide if they want the kids to hear dirty jokes or not. They have an ice skating show too which is amazing. I loved it. I was never bored and like I said, I act like a teenager and bore easily. The ship is huge too so they can spend a day exploring everything. We had so much fun participating in all their acitivites. We never slept because we were always doing something.
We splurged because it was our honeymoon and got a room with a balcony. It was awesome. I don't know for sure, but I think rooms without a balcony are still affordable. Ours with the balcony was. I think 60% of the rooms have them so they don't charge as much as ships with only a handful of rooms with balconies. They even have interior cabins with windows that face the promenade which is this huge mall area in the middle of the ship. They have a sports bar with fooseball and air hockey (everyone can go in no matter what their age), they have shops, they have a cafe with pizza, sandwiches and dessert available all the time and they have parades down the middle of the promenade which are fantastic. It's like Mardi Gras.
Royal Caribbean has three other ships just like the one we went on. The Voyager of the Seas was the first one to come out, then came ours ( the Explorer) and the Adventure and the Navigator are also just like it but I don't know which one is the newest. The rooms are really nice too and the staff and service was amazing. My hubby and I are really plain, picky eaters so the food was fine to us but if you're a real food critic don't judge the food by what I say. We loved it. My hubby ate hamburgers, hot dogs and pizza in the buffet area almost every day. These ships are the largest ships in the world and they're all new (the Voyager is the oldest and I think it came out in '99) so they're all very nice. I loved it and refuse to go on any other type of ship because these spoiled me so much!!! Good luck.