At VLC, stay airside—compact terminal with cafés makes staying put the safest option.
Take the metro from the airport to Colon (20 minutes, EUR 4.90). Walk 10 minutes to the Central Market (closed Sundays). Spend 30 minutes inside the market looking at the stalls and buying fruit or local produce. Walk 10 minutes northwest into Barrio del Carmen for the narrow streets and street art. Return to Colon metro with 40 minutes to spare.
Follow the Central Market and Carmen route, then continue 20 minutes east to the City of Arts and Sciences complex. Visually it's one of the most striking modern architectural sites in Spain. The Oceanografic aquarium costs EUR 33. The Hemisferic IMAX costs EUR 9. Walk back through the Turia gardens (old river channel converted to a 9 km park) to reach the metro. For lunch, La Pepica on Paseo Neptuno is the classic seafood and paella restaurant from EUR 18.
With 10 hours, add the beach at Malvarrosa (20 minutes on tram 4 from the city center). The waterfront is calm on weekday mornings. Alternatively, rent a bike from Valenbisi docking stations and cycle the entire Turia park from the Cathedral end to the City of Arts and Sciences.