Man, I haven't been to Primanti Bros. since...yesterday! It's in the Strip District, which is an interesting area in its own right. A nice place to stroll around on a Saturday morning.
Ride the incline at Station Square (across the Monongahela River from downtown) and enjoy the view of downtown from Mt. Washington (better at night).
See if you can finish an order of large fries from the Original (right next to Pitt, your friend will know where it is).
You can check out pittsburghlive.com for other ideas.