Try Al's for your Italian beef sandwich on Taylor street. Order with or without sweet or hot peppers, or both as I do. It's an Italian restaurant row not far from the Crowne plaza hotel I suggested on Halsted & Madison. You can walk to Al's (a mile +) and after your sandwich & fries cholesterol bomb, you can cool off with an Italian lemon ice at another vendor.
http://www.alsbeef.com/company/locations.asp
For a Chicago style hot dog try Gold Coast Dogs.
http://www.goldcoastdogs.net/
And if you like street food try to get a Polish sausage. Polish Sausage served in a Hot-Dog bun with golden brown onions grilled in butter and a splash of mustard. Back in my younger days, This vein clogging delight was a 3am treat after an evening of dining & drinking. You would head South on Halsted to the Famed & Historical Maxwell St. Market area.
http://en.wikipedia.org/wiki/Maxwell_Street
Again, not too far +- one mile from the Crowne Plaza. It was a rough neighborhood back then. You would order at the sidewalk window and jump back into your car & lock the doors for fear of being accosted by street vendors selling XXX video tapes & fake gold bling. Today the area has been completely gentrified with 1/2 million $ Town-houses & Condo's interspersed with Starbucks and the usual that go along with modernization. The original Polish sausage place was pushed out. But you will still be able to chow down this original at:
http://www.jimsoriginal.com/jimsoriginal/Welcome.html