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Who do we contact within the university? The psych department head?
You may wish to check the website of the local university.

For example, University of Oregon Department of Psychology lists its clinic services, which do not seem to include IQ testing.

Oregon State University College of Liberal Arts School of Psychological Science lists many areas of research but does not seem to list a clinic.

Pacific Oregon University School of Professional Psychology lists Assessment & Testing Services in Hillsboro and Portland through its Pacific Psychology and Comprehensive Health Clinics.

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I'd like to know if anyone has had a good experience using a local university to test their child.
I've heard of positive assessments and insightful reports. However, this may depend upon the family's reason for testing, and the tester's familiarity with the circumstances which your child presents with. It is often posted that the assessment experience is most beneficial and insightful when conducted by someone familiar with giftedness.