Slight nuance to the thoughts so far: I’d avoid the racks close to the street at 5th and Indiana/D; they are pretty close to the curb, and police vehicles often back into those spots. The one time I parked there, I was about 1 inch away from having who knows what kind of damage caused by a police wagon backing into my locked up front wheel. There are more racks closer to the courthouse entrance without that problem.
Another close by parking option are the racks outside of the main Department of Labor entrance at 3rd and C NW (in view of the front entrance/guards, as well as the roving guard).