I think any fan of Disney will like a
Disney cruise.
I do have to say that my early cruises, I loved. I've been on all 4 ships and my next one will be #10. I still have a good time for the most part, but I have seen so many changes, that I can't say that I love them anymore.
Most of my cruises have been adult only and a majority have even been solo.
You can avoid the children on the cruise for the most part. There is an adult-only area on the pool deck. There is an area of clubs that become adult only after 9pm. There are a variety of wine, cocktail, and spirit tastings that incur an additional expense. These are fun and I believe, a good value, so I highly recommend these. There is no cocktail/spirit package like on other cruise lines.
I'm probably in the minority on the daytime entertainment. I'm not one to play Bingo and I'm not interested in trivia, so I don't participate. Usually, I'm outside enjoying the sunshine with a good book or taking a nap on the Promenade deck. Occasionally, there will be a movie on that I haven't seen in the theater. Sometimes I will sit in the coffee lounge(adult only) and enjoy a treat there.
Evening entertainment will be either the Disney Broadway-type production show or a entertainer from shoreside. I have enjoyed the production shows, initially, but not enough to see them on repeat cruises. They are G-rated, FYI, and are Disney story-related, for the most part, rather than just song and dance. The shoreside entertainment will usually do an extra adult-only show in one of the clubs, but they are PG rated, not R rated.
Evening in the clubs is usually dancing and maybe some kind of game. There is a sports bar, if you are into that. Here again, PG rated, for the most part. The clubs will most likely be deserted by 10:30-11pm.
The deck parties are live musicians with the characters dancing and the cruisers, either dancing or enjoying watching the dancing. They will show some animated action on the big screen and then there are some fireworks at the end. You can dress like a Pirate or not for Pirates in the Caribbean night.
I find the mixed drinks aren't very good, so I avoid those.
I find most of the public areas to be loud. The deck parties are loud, the atrium is loud, the dining rooms are loud.
If you want to avoid the kids, try to steer clear of the atrium where most of the character meets are held. The kids and families do have their own pool, so you can avoid walking through that area, if you want. Their clubs areas are easily avoided.
You can look at past navigators at
http://disneycruiselineblog.com/personal-navigators/ to see if there are enough adult activities to keep you entertained. Since I don't care to participate in most of these activities, my answer is no, but then that's because these don't interest me. They may be just what you are looking for and there are plenty of people that will tell you that there is so much to do, they can't do it all. Only you can decide that for yourself.
My worst kid story...one night I wanted to see the late movie on the Funnel Vision and it was the exact same night that the kids from the club had a late night pool party. I could not hear a word of the movie. So disappointing since the movie would not be repeated during the cruise.
So, I wouldn't let the fact that there are lots of kids on a Disney cruise bother you. The adult activities aren't to my liking, but may be fine for you. Adult beverages can be had. Definitely budget for the tastings and you may or may not like the cocktails, but there is always beer, wine and dirty martinis!
We have sailed about 20 times on NCL, RCCL, Carnival, Princess, Celebrity, and our first Disney cruise this Thanksgiving. We usually choose based on the ports of call and look for the best ship/itinerary we can find on specific dates as we are tied to the school calendar. 
It is a matter of what would "ruin" your vacation, or what you could overlook.
