Worry not! Puerto Andratx is delightful. Someone described it as the nearest thing to a Cornish fishing village and I can't think of a better description. It's very scenic, has its own small fishing fleet where you can watch the fish being taken off the boats, loads of harbourside cafe/bars and restaurants and a marina with lots of smart yachts. As it is also a sought after place for the local population it does not get that 'closed down' out of season feel that a lot of purely tourist resorts get in winter.
'Le Cafe' is well known as one of the best and busiest restaurants and Sunday lunch at Villa Italia is delightful. Though I'm sure everyone has their own favourites.
However there is hardly any beach to speak of, which is why there are so few hotels and it's not in the main travel brochures. If a beach is required the best one is a 10 minute drive away.
Also anyone looking for nightclubs, entertainment etc may well feel that it is too quiet. The nightlife consists of the many, many restaurants perhaps followed by a bottle of vino whilst people watching at one of numerous smart cafe/bars on the harbourside.
Hope you have a good time.