I did that tour a bunch of years ago and yes, good cheesy fun is accurate. Looks like they’ve upgraded from the black-painted school bus I remember!
I still have the souvenir magnetic bullet holes on my fridge!
Wow, I bet I passed right by there and had no idea. I’m planning / hoping to take a trip soon - I’m shooting for next spring since my plan for next month got dashed - and I look forward to all the stuff being mentioned here, especially The Untouchables Tour.
Al’s on Taylor Street (only that Al’s, not the franchise locations) would be the obvious choice. And go across the street for some Mario’s lemonade (if it’s still open for the summer–I can’t remember when it closes, but I think it is some time this month. Last time I was in the neighborhood, about a week ago, it was still open.)
If you must get a beef somewhere in the Loop, Luke’s on Jackson is probably your best bet. Most of the beef stands I would recommend are well outside the downtown area. There’s also Mr. Beef on Orleans, which is usually in the mix of best Chicago Italian beefs, but it’s not necessarily one of my favorites. (My favorite would be Johnnie’s in Elmwood Park.)
ETA: Oh, and there’s certain ways of ordering the beef. You can get it with hot peppers (a mix called “giardiniera” which is usually celery, hot peppers, carrots, cauliflower, etc., with vinegar and oil, although different places may have slightly different versions. There is a more bare-bones version as exemplified by Pop’s and Chickie’s that is just celery and jalapenos), or you can get some cooked sweet green peppers on it. Or, as I like to order it, “hot & sweet,” which has both. Then there is “dry,” “wet,” “dipped” (and maybe “regular.”) Dry has no additional jus. Wet has more jus than the regular version, and “dipped” is dipped in the jus, to make a very messy, but delicious sandwich. My order is always “Italian beef, hot & sweet, dipped.” You can also try a “combo” which is an Italian beef with an Italian sausage nestled in it. That’s a popular item, too.
What about the houses designed by Frank Lloyd Wright?
I will be staying in Libertyville so no place in the area is out of the question. Italian beef sounds as complex as chili in Cinncinatti or barbeque in Memphis. 
There’s a little primer here from Al’s on how you can order them. You can also get it with cheese, and some places (mostly those that don’t specialize in beef, but are just general hot dog stands) give you the option of barbecue sauce–usually that’s just called “BBQ beef.” Do not confuse this with actual barbecue. There’s a little more on it here. The terminology can vary a little bit, but everyone seems to understand “dry,” “wet,” and “dipped.” Some people say “soaked” or “juicy,” and you can even ask for it “double dipped,” but it’s wet enough dipped (I mean, the whole thing is dipped into the pot of jus.)
FLW tours in Oak Park are very good.
Yaeh, and if you end up there, Johnnie’s for a beef is a short drive away!