Plenty of really good deer hunting near Pittsburgh. However, the closer you are to the city the more crowded the public land hunting opportunities will be. Not sure what area of Pittsburgh you are in, but I know that there is public game lands north of the city in Wexford area, also hunting is permitted at Hillman State Park, and portions of Raccoon State Park. Also some game lands in Washington Co. within a short drive. I'm originally from West/South Hills of Pittsburgh so those are the areas that I am most familiar with. As others have stated, the Hunter Access Program is good also. They're private lands, and you do need to get permission from the land owner, but they've generally entered into an agreement with the game commission to allow some form of public hunting access. They'll generally be less crowded in my experience.
Hunters Ed. Class is your first step. Like I said, I'm from Pittsburgh originally so feel free to send me a private message if you need any more detailed information.