Buckets and buckets of rock art! And some lovely tombs. Where's Annexus Quam when you need him?
I'll look a few bits up and post at the weekend.
How about ... a bit out of the way, but ...
Santa Cruz - Cangas de Onis, 60km E of Oviedo : a decorated chamber covered by a large tumulus upon which is built a chapel. The monument is preserved below the chapel and can be reached by a ladder! The decoration is painted and carved.
http://www.el-caminoreal.com/monumentos/dolmensntacruz.htm#
http://www1.las.es/~fmiranda/la%20historia.htm