To go out for a drink the island has a great number of bars and pubs scattered everywhere, which are lively and friendly and usually quite small in size.
As for clubs in Majorca and discos in Majorca, for night life fun, you have to go to the "Paseo Maritimo" in Palma, where you will find a concentration of most of the night-life in Mallorca. Other urban centres such as Pollença, Llucmajor, Magaluff and Alcudia also have their own night-life.
If you just want to surf the net, we have several addresses of Cybercafes, as well as an events calendar with evening shows and concerts in Majorca