Definitely stay on 79 and then take 376 to the airport when you hit it south of Pittsburgh.
Oh, for everyone else who responded who used to live in Pittsburgh. You may have been confused about why they would take 376 at all and go through town. The Parkway west in now called 376 from downtown until it connects to 80 west of 79.
Instead of having at least three route designations for the Parkway west, 279 from town to 79, 22/30 from 79 to the connection with 60 and then 60 from there, about 4 months ago they officially renamed it the 376 corridor.
Here's a map showing the re designation.
http://maps.google.com/maps?q=pitts...20045,-79.848633&spn=1.380129,2.90863&t=h&z=9