Andratx is a very relaxed family resort. The selection of nightclubs here is quite limited. If you're looking for something more lively, check out Palma Nova or Magaluf, just 15 minuetes away east of Puerto Andratx.
One club in Andratx well worth checking out is Barracuda. It's very popular with tourists, has a fun atmosphere and plays a mixture of both popular Spanish and international dance music. This is a great place to meet people (from all over!).