If yo can walk a little, go 3-4 blocks past the courthouse, and turn right. There are a few free 2 hr. parking spots on that street, on the left side(one way). Do not park in the bus pickup lane on the right side of the street.
You will have to go throught a police metal detector and empty your pockets to get in, so watch what you take with you to the courthouse. They will confiscate knives and any weapons at that point. I forgot and had a small pocket knife(2 1/2" blade) that I've been carrying for over 30 years and they took it, tagged it, but returned it as i exited the courthouse.