Here's a route, Millvale to Hays Eagles via Point State Park. It's almost entirely car-free, so low stress. It follows: North Shore Trail, Fort Duquesne Bridge walkway, Fort Pitt Bridge sidewalk (narrow) looping around on narrow sidewalk to the Southside Trail past Station Square (go slow there, watch for small kids), past Hot Metal Bridge continuing upstream. This is not the fastest route, but it's probably the most pleasant.
https://ridewithgps.com/routes/23172152
The alternatives and their disadvantages:
- If you cross Allegheny before Fort Pitt Br (6th St, say) then you're on busy streets with lots of cars and lots of traffic lights to get across downtown.
- If you cross Mon at Smithfield St Bridge instead of Fort Pitt, then you have to bike on Boulevard of the Allies or other streets -- more traffic lights, more cars.
- If you stay on the right (north) bank of the Mon using the Eliza Furnace Trail, you can cross at the Hot Metal Bridge, which is very nice, but you've still got Blvd of the Allies to deal with, and biking the EFT is loud and polluted due to nearby cars, while biking the Southside Trail is quiet and green.
Alternatively: ask around, find Yale, ask him to show you the route.