The network of public transport in Valencia is quite good and offers several ways to move. The metro connects the city to the airport and is the best way to reach the villages in the neighborhoods and the beach, meanwhile the buses, which are always circulating, serve all districts of the city. The taxi is also a good way to move, especially on night: the valencian taxi-drivers use to apply special tarrifs on night, particularly economical if you can share the cost with someone.
Anyway, the best way to going around the city of Valencia is the bicycle. Valencia can count on 130km of cycle lanes and on Valenbisi, a recent service of share-bike continually improved. The annual subscription costs 18 euros and is active 24/24 hours: thanks to it, you will be able to take your bike to one of the 275 stations around the city. There are more options if you are not intrested on an annual subriscription.
From Valencia leaves also a lot of trains and autobuses to the other cities of Spain.