To your first question, there is a walkway that goes under Lake Shore Drive and over the tracks, which connects Soldier Field to the area by the Gessner House. It's shown in the center of this map:
https://www.google.com/maps/place/1800+S+Prairie+Ave,+Chicago,+IL+60616/@41.8581774,-87.6178819,260m...As to the Driehaus, it is about 7 blocks from the John Hancock, so that is definitely walkable.
These are not bad areas, although I'd at least be on my toes across the tracks from Soldier Field. But they are not the "bad part of town".
As to FHU CGs:
There is train service across NW Indiana to one of the downtown stations. It's possible there is a campground somewhere out there that would not be far from one of the train stations. If you can get a ride to the local station, from there you can get into the city. Check the schedules as they don't run a ton of them. It's called the South Shore Line. You might start a separate thread asking about CGs near the South Shore Line.
I don't know where you board the Big Bus. Uber is very widespread and affordable in Chicago.
There is a Harrah's casino in downtown Joliet that I know has some RV parking. It's an urban setting, including the lot where the RVs are parked. There is security, though. There is a Metra train station a few blocks away, where you can take the train to Union station in Chicago. I would suggest doing any walking around in daylight there (in Joliet). Downtown is busy during the day but night is spooky, and it directly borders on bad neighborhoods. There might be Uber there, I don't know. There are taxis.
Outside of Joliet, sitting by itself, is the Hollywood Casino. They have an actual RV park. You'd need to get transport to/from the train station.
http://www.rvparkreviews.com/regions/illinois/joliet/hollywood-casino-hotel-rv-resortThere is also a casino in downtown Aurora. Aurora is served by a Metra train as well. The station is called the Aurora Transportation Center. It's across the river from the casino, roughly. Don't know if they have RV parking at the casino, but it is a big complex. It's also an urban setting but a little softer looking than Joliet. At night I'm sure it's the same as Joliet in that it's vacant except for the casino traffic.
Currently RV-less but not done yet.