Getting from the Airport is possible using public transport, but we would recommend hiring a car from Economy Car Hire
Hotel Accommodation in Lanjarón
However if you would like something a bit more up-market, it is worth trying the following:
Hotel Espana - on the main street, nice rooms and a pool.
Alcadima - Used by lots of tour companies, good food and a pool overlooking the castle.
Hotel Accommodation in the Alpujarra
Teléfono: 958763048 (sorry no email or website)
For a more remote village experience, surrounded by brilliant walking country, try Casa Sonia In Busquistar.