The way points of this bicycle route:
South end of Elston. Good road for cycling in Chicago because it has a bike lane basically the entire length.
If you want to head West (or East), Lawrence is the best big street. Belmont, Addison, Irving Park, and Montrose are too busy and don't have bike lanes.
Watch out for this intersection -- it tends to be a mess. At this point Lawrence loses it's bike lane and Higgins is the better choice.
Make sure you catch this gentle left onto Foster Place to pick up Foster Avenue again afterwards.
If you've got a mountain bike, I recommend cutting through the woods here by the Irving Park bus stop.