In Nakagusuku, close to the university, there is a cafe called Rainbow Coffee レインボーコーヒー. It is a nice and cozy place with free wifi. It is a great place to study and relax.
The drink menu focuses on coffee from around the world– you can get drip coffee, espresso drinks, and even tea. I also like the “cup cake”. No, not “cupcake”, but “cup cake”… which here means a pancake in a cup. With syrup and lots of cream. They are all pretty good, even if not good for you! Plus you can get a half-size with the lunch entrees, which are all reasonably priced for about 1000yen. They open for breakfast as well (9am). A nice spot to stop at when you are in the RyuDai 琉球大学 area.