I could go on and on about this!
You must try Spanish Omelette, each bar has their own version and there are good ones and bad ones but by absolute favourite is from Bar Adamo. There is one at the end of Zurriola Beach and you can get a takeaway omelette (pintxo de tortilla) and sit on the wall and watch the sunset - it’s a dream!
You must try the burnt Basque cheesecake. The most famous place for this is La Viña in the Old part
For pintxos, my favourites are the hot pintxos. Lots of tourists will get the cold ones as they are on display, but they should have a menu of hot pintxos too. Carilleras (slow cooked beef cheeks in wine) is incredible. At the moment the old part is full of queues for the bars, but you can go to other neighbourhoods for pintxos to avoid this (Gros over the river or Antiguo) one of my favourite pintxo places is in Gros - Kbzon.
If you want to eat at any of the Michelin star places, reserve in advance. But if you google “Basque Culinary Centre restaurant” you can reserve a table at the culinary university and eat Michelin quality food at a budget - the students have a restaurant as part of their project!
For breakfast ask for pantxineta with your coffee from any of the bigger bakery type coffee shops (tahoma for example)
There is so much to say about the food but you can’t really go wrong with it!