If you take the T. it has four stops, First Avenue, Grant Street/Steel Plaza, Wood Street and Gateway center. The closest to the Federal Courthouse is Grant Street/Steel Plaza.
The Grant Street/Steel Plaza stop has both elevators and escalators. You have to look for the Elevators, it is restricted to handicap people, but one exists at Grant Street/Steel Plaza.
When the subway first opened, you could have taken a side line to the Pennsylvania Station and then walked to the Old Post Office Building (Which contains the Federal Courts) on Grant street. The line stills exists, and some people have plans for it, but no LRVs have run on it for over 20 years.
Today, you have to exit the Subway at the Grant Street Exit (the Second stop AFTER crossing the Monongahela River). You have the option of three exits, the first is onto Grant Street, the Second is up a fleet of stairs to Sixth Avenue.
The Grant Street/Steel Plaza stop has three exits. You go the escalators to get to all three exits. The first exit is the easiest to describe, you go to the top of the escalator and turn left and follow the hallway to the Grant Street Exit. Once out of the building turn Right (in the Direction of the Allegheny River), cross Sixth Avenue, then go by the US Steel Building, then cross Seventh Avenue, then you are at the US Post Office/US Court Building.
The Sixth Street exit is the opposite direction of the Grant Avenue exit once you are at the top of the escalators. You turn right, go up a flight of stairs onto Sixth, then across Sixth and walk down Sixth to Grant, then turn Right by the US Steel Building, then cross Seventh.
The last exit out of the Grant Street station is the one I would recommend. You go in the direction of the Sixth Avenue exit (i.e. turn Right at the top of the escalators), but instead of going up the stairs to Sixth Avenue, you go down the escalators to the left of the stairs (There is also a flight of stairs down along these escalators). Take the escalators DOWN, and take the Tunnel to the US Steel Building. You avoid having to cross Sixth Street, but you still have to cross Seventh Avenue to get to the Federal Courthouse/Post Office Building. It has a lot of bends and turns, but you will reach another escalator, go up them and exit the US Steel Building. You be on Grant Street, but only have to cross Seventh Avenue to get to the Federal Courthouse.
More on the Grant Street Station/Mellon Center Station/Steel Plaza Station (All three names have been used over the last 20 years):
http://en.wikipedia.org/wiki/Steel_Plaza_(PAT_station)
http://pghbridges.com/pittsburghE/0585-4477/panhandle_tun_HAER.htm
I am sorry, driving downtown Pittsburgh is possible, but it is easier by Streetcar (LRV) or bus.
PAT Bus Schedules:
http://www.portauthority.org/paac/SchedulesMaps/TripPlanner.aspx
PAT "Trip Finder":
http://www.portauthority.org/rt/1.pdf
The LRVs/Buses start to run about 5:30 AM.
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