Pasadena is a city in Los Angeles County, California and a suburb of the Greater Los Angeles Area. To the west, it is bordered by Glendale (more from Wikipedia). It is home of the private university "California Institute of Technology", commonly referred to as Caltech.
The guys live at Los Robles Avenue in Pasadena and work at Caltech. Penny works at the Cheesecake Factory. They Pasadena City Hall can be seen outside the window of Leonard's and Sheldon's apartment.
The guys frequently go to restaurants in Pasadena, such as a Sushi bar and P.F. Chang's China Bistro (0101, 0315).
When Leonard tries to help Penny to get over her insecurity of not graduating from college, he suggests she'd go to the Pasadena City College (0201).
Leonard gives a talk about a paper he has written together with Sheldon in the Pasadena Marriott (0109).