Unfortunately, it looks like you're riding through the near west side at midnight. Which isn't bad, just spooky. Here's how I'd do it:
Side streets east through Oak Park to Ridgeland. It doesn't matter which ones.
Ridgeland to South Blvd.
South Blvd east to where it turns into Lake, then Lake to Kedzie. Bring a good light, seeing glass is nice.
There are many other routes, but my preference (especially at night) is arterials because they're lit better and get me to my destination faster. Oh, and Lake is a ghost town at night.
I second Lake from Oak Park to Kedzie as the best route.
In the winter, though, be careful riding Lake during freeze/thaw cycles. There can be a bit of black ice in the bike lanes heading east into the City given how the light hits the pavement due to the L overhead. Also, Lake can be plowed somewhat poorly after snowstorms. Using Washington/Warren to get to and from Kedzie on those days can be a good back up plan.