On the important topic of Italian Beef and Chicago hot dogs, there are lots of good places, like Al's Beef, but the biggest players are Portillo's and Buona Beef. Both are excellent. I slightly prefer Buona for Italian Beef sandwiches and Portillo's for their Chicago-style hot dogs. Buona has some of the best fries I've ever had. Overall, I prefer Buona Beef.
If you're not familiar with our Chicago-style hot dogs, they're an all-beef kosher hot dog on a steamed bun, preferably with poppy seeds. It will be topped with mustard, onion, sweet pickle relish ( optionally electric green), dill pickle or sometimes a cucumber spear, sport peppers, tomato, and the defining ingredient -- celery salt. It's acceptable to eliminate ingredients, but adding ketchup is Chicago hot dog heresy.
Italian beef is one of the true Chicago foods. Deep dish pizza gets all the press, but it hasn't been all that popular since the 1980s. Italian beef sandwiches have been a Chicagoland institution for decades and they're hard to find outside of the area.
When ordering a beef, you have some say in how much of the "gravy" (think au jus) is on the sandwich. The normal way just has the gravy that clings to the beef. Or, you can get extra gravy that's ladled onto the sandwich. Finally, you can get it dipped or, as Buona calls it, baptised. The entire sandwich gets dunked in the gravy. Although delicious, it can be messy. You do not want to eat an Italian beef in your car.
You have the option of adding cooked sweet peppers or mild or hot Chicago-style giardiniera, which is pickled vegetables and olives in olive oil. I personally order mine with extra gravy and mild giardiniera.
You may also see the option of a combo, which is both Italian beef and grilled Italian sausage. It's really good, too, if you're man enough.
Portillo's is also known for their Cake Shake, where they literally cut a slice of chocolate cake and blend it with ice cream to create a shake. Over the top sweet, a zillion calories, but delicious.