You can have a great time in the lounges and not drink. Your daughter will be able to go to the lounges if she wants. They don't card people at the door to see if they are 21. She just can't buy booze once inside. There is no requirement to buy drinks just to occupy a table. It isn't like a night club on land where you have to buy something in order to stay. The bands and acts on cruise ships are normally very good and the big production shows are excellent.
If you can afford it, Atlantis is a fun place for the day. It is easily the most popular place on Nassau. Now, please be aware that Nassau has it's share of pan-handlers and in the port area you will encounter some. This type of thing is not allowed in Atlantis. Nassau is a safe place but you do need to keep aware of your surroundings, just as in any U.S. city.
Also, realize that the Majesty OTS is now the oldest ship in the Royal Caribbean fleet. I'm not saying it is a bad ship, just that you may encounter an odd odor here and there if on lower decks and might see some things that appear 'dated'. It is still a great ship and has a loyal following. Majesty was the first Royal Caribbean ship I cruised on way back in 1993 when she was new. If you have a standard outside or inside cabin, don't expect it to be the size of a motel room because they aren't. They are a very snug 119 square feet, including the bathroom. But despite the size they are very functional and good enough for a short getaway. You aren't in the cabin much anyway.