I agree with Salty. I've lived near Beacon and Shady for 20 years and ride all the roads people mention here all the time. It's all perfectly ridable in this area. Somtimes it's messy but it's fine.
If I were headed to Shadyside Hospital, I'd probably choose Shady Ave to Howe or Walnut across to Aiken. Watch for doors in Shadyside--narrower streets. Study the map a bit because there are lots of ways to switch the route up if there are issues on a particular day. Wilkins is okay but Shady offers more "buffer" on bad weather days.
Magee is a bit more complicated to get to because of the one way issues with Forbes and Fifth. Both of them are ridable, but they are also full of buses and traffic etc, though you can get used to it. To work the easiest route is probably Darlington and through Schenley Park and swing toward the Blvd. of the Allies before Phipps. You could go through the Anderson Playground to miss the bridge if you want, but then out onto the Blvd. The Blvd is busy at times but this is just a short stretch, there is space, and the lane markings are good. The right turn into Halket street is popular with cars but fine.
Reversing that in the evening is not as attractive a prospect due to traffic trying to get to the Parkway. Also more cars headed into the park--but it is acceptable. Personally, I would probably ride Forbes to Meyran, then left on Sennot, right at Bouquet and then the next left at the Katz school and back up into the park.
I'd actually ride Forbes all the way at many times of the day but the bus density in the right lane afternoon is sort of annoying.