Leg 1, Day 1: Chicago to Joliet
Throughout the trip, I used the Cyclometer app on an iPhone to track time and distance. The GPS data showed our actual Day 1 trip was 60 miles.
Cyclemeter App: Distance: 59.60 miles (16.8% of the way)
It was not easy following the transition from the bike path going south from downtown along Lake Michigan to various side roads and bike paths and more side roads until reaching the wonderful East-West bike trail known as Old Plank Trail. So our actual travel distance was about 10 miles longer than shown in the above map.
Below is the last picture before departing. I am wearing my skin-cancer-protecting nose shade, which is more than ridiculous given (1) its overcast, (2) raining, and (3) 830 in the morning.
The ride south from Buckingham Fountain follows the shores of Lake Michigan. It’s a beautiful ride past museums (Field History, Adler Planetarium, Science and Industry), Soldier Field, Hyde Park on Chicago’s South Side, and even harbors and marinas such as shown below. 
The trail then ends on the far south side Chicago. There the ride transforms, as it does again and again, into a side roads adventure through places like Calumet City. Shown below was actually one of our highlight food stops: Panos Big Boy (see details at the “Links” tab). Be sure to try their all beef gyros.
Just behind the store wall in background below was a bike shop with a very helpful, and generous, owner who helped Corky, my riding buddy get his fender and brakes adjusted so they were not creating drag on his front wheel. See Good Speed Bike Shop at the “Links” tab.
After some miles of wandering streets, we were able to connect with a bike trail on the far south side of Chicago. Below is a video clip of a bike trail we caught well south of Chicago prior to reaching (by yet more side roads) the long Plank Trail to Joliet:
After numerous subsequent side road and other bike trail adventures we reached the fabulous Old Plank Road Trail, that runs east and west just south of US 30, and brings us all the way to Day 1 end, Joliet.
One of the towns along the Plank Trail is Frankfort.
We spent the night at a motel on the west side of Joliet, several miles off the Route 66 track. Joliet has a river that runs through it; it was a very steep climb on the other side to get to an area with motels and restaurants.
Day 2 here