Going down to Denia and the rocky coast just south is really a good idea.
As for the city, the "Ciudad de las Artes y las Ciencias" deserves a visit, some very futuristic buildings and the Oceanografic is quite nice too. The center I recommend too, the area around the Cathedral in which you can find the "actual" Holy Grail, though I find more interesting gorier things like the mummified arm of St Vincent...
For food, Valencia is the land of rice, home of the world-famous Paella
, though there are other quite enjoyable rice dishes like Arrós a banda, Arrós negre,
etc. For lunch I would recommend a dish of rice in one of the restaurants in the Las Arenas beach, like "La Pepica" or "La Rosa", it is one pleasure to have a Paella at the sight of the sea. For something more informal you can try having tapas
, for example in La Pilareta
a very traditional bar with mussel shells on the floor - though I am not sure if an Anglosaxon stomach will stand that!!
; this place is in Pza del Tossal, not far from the Cathedral in an area with lots of bars and nightlife. If you understand Spanish and are really interested in food, buy a "Cartelera Turia", it has a restaurant section which covers from the best& expensive restaurants to the most budget alternatives.
And do not forget to have a glass of horchata
, quite refreshing and delicious local drink, especially in hot days like you will probably encounter here.