You can run many searches in many different places, but, if you're looking to see what others can see about you, begin by looking where they would look and not spend too much time with the ones that would only be accessible to you or the police, such as an official arrest report. Arrest reports have restrictions since they're not convictions, and have policies in place by the department to request them. If you are are looking for a specific criminal record that you are concerned about others finding, even if it doesn't show up on all criminal background searches, you can go directly to the source of the record and see if it is accessible and how easy to find. Criminal court records are a good example, open to the public and can be accessible, but, may not appear in some or any background checks.
Sep 16, 2015