How's this (actually the reverse of my routine trip *into* the city): Cross 40th St Br, get into Millvale, get on Babcock (past Hardee's and Rita's), ride to where Babcock and Three Degree meet. Babcock peels right; 3D goes left; in front of you is a car wash. There is, however, a third option.
Duck around the left side of the car wash, and head into the trees in the back. What you're on is the old Harmony Trolley line, gone since 1930ish. Not 200 feet in, you'll find a pond, replete with ducks, frogs and other wildlife. Sit and bask in the wonder of it all for a while. The path itself is actually pretty well maintained, lots of gravel in some of the muckier places.
A half mile later, a suburban street dead-ends from the left. Take it, and wiggle up to Perry Highway, and go left (south). When you get to Willi's Ski Shop, go past it and turn right on Graham. This avoids a nasty, narrow, uphill, heavily traveled piece of Perry. At the top, you're back on Perry, but it's relatively level and a lot calmer.
Continue into West View, turning right on Center. (*mild plug* Scholl's Bike Shop is on the diagonal left corner if you need anything.) Cross I-279, ignore the right just after the bridge, but turn right just after that. This takes you into Bellevue. Left at Classic Chevrolet, and you're on Calif Ave.
You can take Calif all the way into the North Side (I've raced the Route 500 bus from here into town, and won, twice), or duck down Antrim onto Woods Run and pick up the river trail, taking note to get off it before the casino and snake your way through the maze of streets to get back over to Allegeny Ave and Heinz Field. Also, swalfoort has a thread from back about a year ago about "Bellevue to Downtown" or some such, in which she describes how to use Shadeland to get across Woods Run and thus get into town. Let's just say that there are several decent ways to do it, all of them useful to know if you're up in this end of town.
From wherever you find yourself on the North Shore, find your way into, through and past Downtown. All told, it's about 30 miles.