Hello, Andalucia is very big and has a lot of interesting nature places. Cazorla, Sierra Nevada, Sierra de las Nieves, Sierra de Aracena, Sierra de Grazalema, Parque de los Arcornocales, Sierra Morena....
I only know a little bit of Sierra Nevada (the central nucleus have highest mountains over 3000mts, very rocky and no vegetation). And Cazorla, it's very touristic and beautiful, lots of pines and deers. I think both are difficult to get in public transport. Normally it's forbiden to camp by your own, but there're camp sites and the weather is nice, so you can also sleep just without a tent.
About beaches, in Almeria they're beautiful in the natural park area of Cabo de Gata and many of them have no houses near, so I guess they will be almost empty during the night, although during the day people will arrive everywhere.