I think you probably would enjoy it, but pick your ship carefully.
Smaller ships may not have enough for kids to do, unless they are happy to join the kids club - in which case, they'll have a blast. Larger ships tend to have lots of activities/entertainment without having to use the kids club. My teens spent the whole time playing mini-golf, shuffle board, giant chess, table tennis, going on the water slides and the ropes course, watching films on the top deck. They never even got to the kids club, and didn't miss it. There's usually a gym, and possibly a sauna, but often this is for older teens and adults only, so you'd need to check that.
My teenagers absolutely loved the two cruises we took them on. We've also been on quite a few on our own, without the kids.
We prefer NCL, on the larger ships if the kids are with us. There's plenty to do, and it's usually not a problem to find a quiet spot to relax in the sun or shade.
Cruise ships aren't particularly good for swimming, the pool are usually quite small and can get crowded, but they're fine for a quick dip. But loungers by the pool are very difficult to get. We mostly swam in the stops we made, as some ports had swimming pools, or we went to the beach.
Food is usually good to great, at least as good as all-inclusive in my experience, and you usually have the choice of table service restaurant or buffet every day, sometimes for breakfast and lunch too. The buffet can get busy, but we rarely use it, preferring most of our meals in the main or speciality restaurants. Whenever we've done an AI hotel, restaurants have been limited to one or twice a week, with the buffet the rest of the time, so cruises are better for us in that respect. We also like NCL in this respect, as there's no set dining times, and you can have your own table. We get up to 4 visits in a week to the speciality restaurants included in the package.
With regard to drinks, you'd need to check if these are included, can be added on as a package, or bought as you go. It can make quite a difference, depending on how much you are likely to drink. Also check if gratuities/service charges are included, or are in addition, as these can also add up.
Port stops can be as long or as short as you want. Some ports can be quite far from the main town, but it's usually not difficult to grab a taxi or shuttle bus. And many ports are close enough that you can walk.
Overall, we love cruises, and getting off the ship to a different port/city each day can be great. There are some wonderful views too as you arrive/leave each port, or sail along the coast.