Which direction are you coming from? Cheapest would be to park at the Casino (free) and take the T (free) to Steel Plaza

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First Ave Garage is just down Grant St and around the corner. Not terribly expensive for the convenience.

Mellon Square Garage would be my 2nd choice but that's a bit of a tight Garage.

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Drive a beige/white Impala, park next to their unmarked cars over by the Sheriff's annex.

you could probably find street parking down along 1st or 2nd ave near the jail too, would only be a few $ an hour and definitely less expensive than a garage or lot.

I would park at the garage near PNC park and take the T over to Mellon, right by the Courhouse. The T is free between the north shore and downtown.

You can also park for free at the casino and take the T over (maybe throw a few bucks in a slot machine on the way out).

Try the iParkit app or ParkWhiz. It will tell you the prices of the garages. I used it when I had jury duty earlier this year.