Yes, California State University, San Bernardino (CSUSB) is located in the city of San Bernardino, at 5500 University Parkway, San Bernardino, CA 92407. The campus sits in the northern part of the city, at the base of the San Bernardino Mountains.
The confusion sometimes arises because "California State University" is the name of the 23-campus system (headquartered in Long Beach). But CSUSB is a distinct campus within the city of San Bernardino, not just the county. It serves ~20,000 students and is a major institution in the Inland Empire.