Valencia is a major city in Spain. It's an easy city for hitchhiking. There are three main highways to Barcelona (AP7), Madrid (A3), and through the South coast to Alicante, Granada, Sevilla (A7, AP7).
There is a roundabout just where the highway 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 highway' (A7) through the center or the toll-highway 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 metrostations Jesus or Xativa. See here a map of the location of the roundabout in Valencia.