Daily tickets: there is indeed a zonal fare system around Valencia, but I am not sure how far it extends beyond the raillines. Many of the local lines used to be real trams till not that long ago, nor if it does offer real savings. Real trams on the street run in the northern part of town.
Airport is served by a kind of turned into metro line with higher airport fare.
Another goal might be Castellon, some 50-60 Kms north which has a fairly new and Spains only TROLLeybusline.
Just checked-out of interest-these sites and since I was there quite some time ago, the system has changed completely and gone over to the usual chipcard-style. For the CITY there are 2 zones (airport is an extra higher priced 3d zone), it has T-dia daytickets, valid on all means, but IN city-area only. See metrovalencia.es. A ´carton´ card may be used more times, but only for exactly same type of ticket.
If you also aim the usual touristy sites, there is also the Valenciacard, includes various entries etc.
RENFE-cercanias around has its own fare-system, also based on zones, with the usual fairly cheap singles or returns. Note that many of the suggestions above range well out of its area. I could not find out if this area now also wants you to load them all onto chipcard (50 cts or 1€ extra to pay on any fare).