Did you notice a lack of quick responses? That is because there is no simple answer to your question. Many times I have suggested Amtrak travel, and people's interest ends with the lack of parking at the Pittsburgh Amtrak Station.
There is no long-term parking at the Station, just short-term "pick up" parking that can be a mess at train time.
The Pittsburgh Parking Authority in 2008 opened the new Grant Street Transportation Center Garage right across Liberty Avenue from the Amtrak Station. Looking at the web site for the Authority, it appears that parking could be $ 13.00 per day at that facility, but I would call 412-288-5569 (day number for that facility) or 412-560-2504 (general information) to find out specifically.
There are other lots downtown owned by another company, but they seem to have limited hours. The airport is miles away, and buses don't connect at train times.
Maybe someone else can add to the information.