How do I mention the quality of my school without bragging

I am currently studying at a US university that is among the top school for the field I'm in (CS). However, the university itself is not well known outside the US, and certainly not as being on par with or better than the more well known universities (Harvard, Princeton, etc.).

I normally wouldn't mind this, but I am currently in the process of applying for jobs back home in Europe and I fear that my application would not get the same attention as those coming from more well-known schools. So my question is:

How do I mention that I obtained my degree from a top school in my field without it sounding braggy?

This would be good to know in terms of a cover letter and in an interview setting.

How do I mention that I obtained my degree from a top school in my field without it sounding braggy?

You use your cover letter. In it, you should brag.

Something along the lines of "I graduated summa cum laude from Tiptop University - one of the 7 top Computer Science schools in the U.S." is perfectly appropriate.

Unless your interviewer specifically asks about your schooling or about your university, there's no need to bring it up during the interview itself. Once you reach that stage, they have already read your cover letter. And if they weren't familiar with your school already and cared, they Googled it already.