Just about all Spanish cities attract tourists, that can't be avoided. But you need to remember that tourists usually ony frequent the historic centres of these cities, so you're unlikely to be bothered by them at university. And most students go to bars, cafes and clubs that tourists are unlikely to visit.
You want to live with "actually Spaniards"??? Here's a tip: Learn some English, first.
Try looking at the university towns. And try starting with the ones that you have access through any program(s) you might use.
Advice: Go for more than 10 months, if you want to become fluent...summer isn't enough for that. If you're only looking for some experience abroad, that will do.
Travel ALL you can.
Avoid the people who speak other languages, but they will be pretty much everywhere.
Immerse yourself...it isn't really going to happen by itself, YOU have to make the effort.
I can highly recommend to study Spanish in Alicante. It is a very nice city on the coast. There are no dialects. I have studied in Elcano Spanish school. There are good teachers, the prices of the courses are very favorable. They also organize a lot of activities and trips and they can offer you accommodation in a shared flat or in a family.
Barcelona, Valencia, and Seville are all very beautiful, but they have a lot of tourists :)
I'm planning on studying abroad for summer 2014, I'm just trying to figure out where I should choose to stay. I want to be able to surround myself with actually Spaniards and be immersed in the Spanish culture, so a city that is not that full of tourists. Plus, any study abroad advice, suggestions, etc, please fill me in, thank you! :)