TheFork users who ate in Paterna have said really good things about The New Chess, Casa Toni and Tapería Hispania - Cortes Valencianas. Maybe you should give them a try!
Some of the more popular Traditional restaurants having a terrace in Paterna according to TheFork users include:
La Vecindad, with a 8.5 rating
Restaurante Alcazar, with a 9 rating
La Motocicleta K7, with a 7.7 rating
In those days what better than a traditional restaurant to retrieve the comfort of eating at home.