Direction Tarragona, Valencia
Possible other untested spots
There is a roundabout just where the motorway starts in Valencia. This is a good place where cars can stop but it is at the edge of the city. You can get rides to Alicante, Granada and Sevilla, either by the 'national motorway' (A7) through the center or the toll-motorway along the coast (AP7).
The roundabout is located on the street '"Ave. de Ausias March'" in the south of the city, close to the river. It is a 15-20 minute walk from the main train station, and metro stations Jesus or Xativa. See here a map of the location of the roundabout in Valencia.
I tried this spot on october 2010, there not really easy area where the car can park, I think they put a security rail here. Anyways, you can find a lift from the station close by at least until the next gas station. If somebody can confirm.