Wow! So many answers from day to day, I was sleeping in the meantime:
No, SF is so desperate for any coding talent right now, you probably wouldn't have trouble getting a job. Now, the housing situation is a different story (https://forum.mrmoneymustache.com/off-topic/bay-area-rental-prices-an-explitive-filled-rant/)
Ok, now that's ridiculous... I'm living in London right now, and it sounds even worse than here. Anyway I wouldn't have any problem adapting to it, it would be ok to live in some town outside San Francisco.
In the US, computer engineering generally refers to hardware/embedded work, while software engineering is used to refer to web work. You should probably pick which to target-- there are opportunities in both.
My studies in Spain were actually 5 years long, and it's not strange to finish them in 6 or 7 years (I did it in 6 studying for a year out in Berlin), so I had time to study both disciplines... Now I will have to choose I guess.
I would probably pick either the Bay Area or NYC, research the biggest employers as well as interesting startups, and start sending out a few applications. Maybe also get in touch with a recruiter.
I think that's a good idea. Because of the weather, as you said, I would probably choose somewhere near San Francisco, since I'm from the south of Spain (it's really warm down there), but I can adapt to the cold without any problem.
OP, I would recommend finding a city where you can get by without a car. It will make your life a LOT easier.
I don't want to have nothing to do with cars actually! I have a driver's licence, but I got it like 5 years ago, and barely have touched a wheel since then, so I have lost all the practice. In my city (Seville) I lived close to the center, so that was not a problem. I know that in the States things are different, like a lot of people use a lot of cars, but I don't even know if I could get one, so...
For the OP, have you considered graduate school? A lot of the really top internships go to grad students. You don't have to be a genius, but you do have to be pretty good. It also helps if you are already working on something related to a project that the company does. The people I know who did internships at places like Google & IBM Research were actively recruited because of their graduate work.
I have thought about it, but after 6 years of studying for just my degree, it's almost like if I had a master's degree (in fact, many Spanish people here in London write that in their resumes). I just want to work now.
Thank you very much to all for your help, this is such a great community!