Where are you staying? In the city?

The most popular in the city long route is the Lakefront Trail that runs along Lake Michigan ( http://www.traillink.com/...lakefront-trail.aspx ).

Nice and flat and smooth path. Can do about 20 miles one way, or more if you are willing to ride through the hood a little bit on the South End. Downside is it is super super super crowded, especially during prime times.

If you want to ride in your aerobars, you need to start at like 5am on a weekend, or either 5am or 9am on a weekday. Otherwise, you can do a road bike - but there are many super busy spots where you are going to be limited to 17mph or so as you pass runners and rollerbladers with dogs.

If you have the flexibility to go to the burbs, that opens up a lot more games...

Not much quality cycling in the city, and I don't recommend going to the south end unless you want to see 13-year olds with semi-automatics trying to score a bike off the path (however I'm aware people will chime in and say it's never happened to them, they ride all the way down south all the time, etc. luckily it's never happened to me either but unfortunately it's happened to many of my friends).

If you can, hook up with some other people and head to the western burbs.

Strava heatmap might help ?

http://labs.strava.com/heatmap/#11/-87.73216/41.83401/blue/bike