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Each state has different rules governing business formation and qualification for out of state (so-called "foreign") businesses. Whether it is "smart" to form a business in a state other than your place of residence depends on the result you are trying to create by doing so. Why were you thinking of forming in Wyoming?
There is a $500 fee to register a foreign LLC in Illinois, so you would actually end up paying more up front (Wyoming registration, plus Illinois foreign registration).