On Friday, you can go to Tula café at Ruzafa borrouht, but first or at last... go to El Rojo, a place for drink and eat jam and cheese (it has the coolest mundan terrace in Valencia) also people is nice. Not posh, it's a kind of tapas bar really. Great place in the nicest valencian borrought.
On Saturday morning, best thing to do is to go to Mercado Central, just for visit, for buy some food; good cheese, fruit, fish... whatever. Great building and area!!