Depending on which way you are coming in you might have a Holiday Inn on the way out. If you are coming from the west then you would get off of the turnpike at the exit for Rt. 28 or Rt. 79 with 79 being the more direct route and much better around rush hour which in pittsburgh lasts from about 4 to about 5:30.
The traffic in the city itself is a mess. This comes from the geography more so than poor civic planning. Pittsburgh is built on a triangle because it has two rivers forming a third.
This is in addition to many hills that make up the city and the surrounding environs.
My advice would be to come a little bit early, maybe take in the Heinz history center, which isn't great but is very close to the cultural district and then go to your show avoiding rush hour entirely.
As you leave, if you take Rt. 28 there is a Holiday Inn just off of 28 on the way up to the turnpike at the RIDC park exit. There is also a Max and Erma's there but it is not open that late.
A better option would be to head up from the cultural district to the strip district which really isn't a long walk and find something to eat at one of the many restaurants or bars up there.
Nearer to the cultural district there are some expensive but nice restaurants but I'm not sure how late they are open.
The area that you are travelling to is pretty safe really. I've walked around there late at night with no problems. There are usually too many people about even later at night for there to be any trouble. There aren't many really bad areas in Pittsburgh overall although there are some. You can pretty quickly tell when you are in one though.
Parking can be a PITA during the day and meeters are $.25 USD for 7.5 minutes but there are some parking garages that charge fairly reasonable rates including one big one right by the Strip district that is about $5 USD or so for all day, or at least all evening.
Traffic is a hassle, it can be really bad, especially leaving during rush hour, but if you are heading into the city and avoid 28 when you are coming in you shouldn't have any problems.
I live in the city so if you need any more specific help don't hesitate to contact me.