Around Case, there are many places that are cozy and quiet that are perfect for actually getting work done, or for napping if that is what you so chose.
1. Basement of KSL
Although you would think the library is the best place to study, it is often either too loud on the main floor or second floor, or disturbingly quiet on the third to the point where you don't even want to unzip your book bag to get out your things out of fear of someone hearing you and staring you down. The basement is often quiet, and was my favorite place to hang out as an undergrad and study/nap.
2. Thwing Reading Room
This is the room that is on the left side of Thwing if coming in from the Euclid entrance. If you immediately go left and up the few stairs, you find an office area. Immediately to the right, there are couches and chairs. This reading area, to the best of my knowledge, is available to students unless it otherwise says reserved for an event. It's quiet, and no one is ever there and it is comfy too.
3. Mandel Center
Past the lobby area, there are couches, tables, and even a fireplace, for you to sit around and get cozy to study or to sleep. It usually is only busy in between classes, and usually on the days there are a lot of social work classes so there are chunks of time where there is only one or two people there. It's closeness to Uptown also is a plus because you can go get lunch or dinner quickly instead of hiking halfway across campus.
4. Coffee House Porch
Although not available right now, this is one of my favorite places on campus. Inside the coffee house is great too, but it can get loud. When the sun is out and the temperature is above sixty degrees, this can be a great place to study while enjoying the warm weather, or to lay back and take a short nap in the sun.
5. Medical Sciences Library
Located in the School of Medicine, you would expect this place to be pretty crowded. But due to the differing schedule of the med school and the other graduate and undergraduate semesters, I have found that it is pretty empty at the end of the semester when I need a quiet place to study the most. One night during the last week of fall semester, I went there and was the only person in sight besides the person working behind the front desk. So if you are looking for a quiet place that is not as intimidating as the third floor of KSL, then this is the spot for you.