I live 20km's from Valencia and it's a great place. Personally I recommend getting the tourist bus, there's 2 now so that you can get your bearings. I did them both recently with friends and found that the one around the marina and F1 circuit was far less interesting.
The Arts and Sciences complex is fantastic for walking around. Within the old town there's some nice old stuff, if you are there on a Sunday the La Lonja (silk exchange) is free to go in and that's a lovely building.
The metro is fairly cheap and gets you around nicely, Malvarossa beach is very nice.
Also the Biopark (Valancia Zoo) is a brilliant half day out. It's very unzoo like and great for photo opportunities. It's on one of the tourist bus routes now.
If you are staying in the city, get the Metro from the airport and save on a taxi fare!
Valencia morning light by
swag72, on Flickr