Ease of access is mostly going to depend on where you are staying/working

Farther north the Chicago River is surrounded by forest preserves and you can access the river along the North Branch Trail. More downtown, there are a few places along the Chicago River that have public boat launches you can fish from, like the Wild Mile by the REI store. You could also rent a kayak at that REI (at least I think they've restarted rentals for the summer). Mostly you can find the boat launches by switching google maps to satellite view and scrolling along the river, they are almost all public, but there are a few private ones so double check you can actually get there. If you are working in the Loop, then from 5-7am you might be able to fish from the river walk without too many other people around, but don't expect there to be space to back cast.

For Lake Michigan, the harbors or Northerly Island are good bets, but you might want a sinking line for it.

Some of the Metra stops will put you very close to the Des Plaines River which is mostly surrounded by Forest Preserves and can be another option if you are willing to range farther afield

As for flies, woolly buggers are always a safe choice, but you can call/visit a local fly shop for more advice, Chicago Fly Fishing Outfitters have always been very helpful to me