Valencia is an easy city for hitchhiking. There are three main highways to Barcelona (AP7), Madrid (A3), and through the South coast to Allicante, Granada, Sevilla (A7/ AP7).
Ruta Costa
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 [Allicante], [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. See here a map of the location of the roundabout in Valencia.