Hi, welcome to Pittsburgh! Wow, I think you've already ridden Bigelow Blvd. more than a large number of us, myself included. It's certainly legal but speeding is a bigger problem on that road than most. There are a number of other routes downtown, including 5th Ave, Liberty Ave, and Penn Ave (probably in order of my preference), or a variety of lesser traveled roads or trails.
Bike Pittsburgh has a commuter map, it's online here or you can pick up a paper version from their office on Penn Ave., or in most bike shops.