Inside the library (if you can even get in) you have restrictions about how many breaks you can take or how often you can go outside. You can try and study outside of the library or in a park, but both tend to be loud and you're limited by the weather.

Most cafes tend to be small and loud, but if your Turkish is good enough to be able to order a few cups of coffee, you might try your luck at the Focaccia Pasta Cafe near the hospitals and across from the library. It's about the only place I've found that's large enough yet not busy enough you might get some work done (haven't tried it myself, not sure how they feel about milking a few cups of coffee, but it's usually not too busy).

In general I find headphones and music helps create a filter for unwanted noise when studying/working.