There are 2 restaurants in Pateo which may suit you. One is O'Leme which is well known for its Stone Steak but does other local dishes. Opposite is Mama Mia which has a selection of dishes. There is also Mama Mia 2 which150 metres away and is also owned by Mama Mia restaurant. Mama Mia 2 does tapas but has only recently opened and I should imagine it is more like a cafe than a restaurant but I have never been in Mama Mia 2 yet will will be doing so in December I hope.
As you are going in December it is always wise to check if the restaurants are open the day you want to visit. Some can be open one night but closed the following night.
These restaurants are just down from Pateo village so very walkable. Look at Tripadvisor for reviews of these restaurants. Mama Mia and Mama Mia 2 are reviewed on the same Reviews page so be aware which Mama Mia you are reading about.