First of, thanks everyone for their helpful posts! www.todopintxos.com is great for recommendations and maps. Note that google maps is in spanish, but most of the street signs are in basque. Also some of the recommended tapas are no longer offered.
In no particular order: (also I do not like foie, or seafood, so I know I missed out on some great places and some great dishes)
This was my favorite place. The owner branched from La Cuchara. The have absolutely amazing beef cheeks, the best out of all I tried (and I ordered it every time I saw it on a menu). Also their risotto (actually pasta, not rice) is really good. Goat cheese with a caramelized something and cherry sauce is amazing. Everything I've had here has been awesome. Also a good place to share plates with friends.
A very "molecular" place. The food is innovative, small, pretty. A lot of the dish is inedible and just for looks. Known for La Hoguera - salt cod that you smoke yourself. This is not the type of place you can share with friends, and a little pricey. Worth going to for molecular gastronomy, you can try a few things for under 20 euro - where else in the world can you do that?
Scampi - gambas (prawns / shrimp) deep fried almost tempura style. These are absolutely crispy, perfectly deep fried. They also do calamari. Really cheap.
A Fuego Negro
A more modern take on tapas, not molecular like Zeruko but I like this place a lot. I tried a caesar salad and the cheese was finely shaven and melted on my tongue almost like flakes of chocolate, I've never had anything like that. The makobe burger is a bite sized kobe burger. They serve dove but I thought it was a little well done. The ros bif wasn't very memorable. The risotto was very good. They have an english menu if you ask for it
Known for their patatas bravas. Good place to fill up on cheap beer and bravas before you go on to nicer places.
La Cuchara de San Telmo
Really great risotto, the beef cheeks were good. A friend that is living here didn't like the place, says he ordered a rib and it was full of fat Maybe this place is a little overrated, but still a classic.
Also a favorite, also one of the few places open on sunday and monday. They do pretty decent beef cheeks, not as good as border berri. The solomillo a la plancha (mini steak) was really great. Grilled duck also great. Risotto was okay. Crepes are great. DO NOT ORDER morro, after tasting it (disgusting) I found out it was snout
Good for wines and ciders (ask the bartender to show you how to pour the cider if you order a bottle, it makes a huge difference) they have a nice steak to share.
I had a lot of fun at a cider house. At this time of the year, there aren't that many open. I previously thought cider from the bottle doesn't taste that good, but cider fresh from the tap is vastly different. It's a very fun experience, we were the only table of foreigners, the old men are obviously pros at catching the cider and will give you a few tips. The food is so-so (where we went, a set menu of salad, bacalao, steak, cheese with quince jam, and tejas and nuts) but a really good unique time. I came back almost sick from the amount of food and cider in me!
I miss it already!