40 mins easy drive down the motorway.
Coastal city of historic importance (due to it's strategic position in the Punic Wars up until the Spanish Civil War) - visit the Roman Theatre, Castle, Roman Ampitheatre, Spanish Civil War Museum etc (you can find details of pricing and various discount tickets for multiple sites at http://www.ayto-cartagena.es/)
Great shops too (including a El Corte Ingles department store) !
Pleasure cruises round the harbour. Nice cafes on harbour's edge.
The area around Cartagena is also famed for it's windmills (see pics) which were used up until 1945, and are now being restored and preserved in some cases (UNESCO World Heritage status). They were originally of the 'alas' (wings) type, but were later replaced with 'velas' (sails). They were used not only to grind cereals, but to draw water from wells.