I think we were away for a week, but managed two trips into the mountains. One by the local service bus to the village of Mojácar - technically we were staying at Mojácar Playa. There is a reasonably informative Wikipedia page about the area but it seems to omit plate tectonics. My half-remembered vague understanding was that an earthquake (I think - might have been a volcano) in relatively modern times had changed the topology of the land, and this seemed convincing when seeing the plains from the hilltop. The village was pleasant enough if dull, the expected range of decent eateries and tourist souvenir shops.
One morning we went on a 'blanket tour'. A free coach trip into the mountains (what mountains? where? I can't remember, this was 2002, I wasn't keeping a diary! Although, I've spotted Sorbas on the map and this rings a bell, so maybe it was there!). The downside was having to sit in a lecture about the benefits of the Mediterranean Diet, and an attempt to sell us merino blankets and shoe inserts - hardly an imposition, and not like the hardsell of Time-shares.