TheFork users who ate in Puerto De La Cruz have said really good things about La Carta, La Viña and Bodegon El Empacho. Maybe you should give them a try!
Some of the more popular vegan restaurants that offer gluten-free options on their menu in Puerto De La Cruz according to TheFork users include:
La Carta, with a 9.1 rating
La Viña, with a 9.3 rating
Bodegon El Empacho, with a 9 rating