There is a lovely new private albergue in the main street of the small town of Atapuerca, with single rooms as well as dorms. (Albergue el Peregrino). A bus leaves every day (I think) at 4.40 p.m. From the town centre to the sites. We had an excellent Spanish guide, who could also speak English, and she had worked on the digs in summer. This town is a better stop than up at San Juan de Ortega, which can be v. cold. You cannot visit the sites unless on a guided tour, because they are spread out around the area.
The museum of Human Evolution in Burgos is also worth a visit, and runs whole day trips back to the sites of Atapuerca. But why go back, when you have already walked through? Also, I was disappointed at the museum to find not one single publication in English in the extensive bookshop on the top floor.