Re-incorporate, foreign qualify or new LLC?
Generally speaking, when a company owns any physical property, such as real estate, the company must be registered in that state, respectively. In this case, the company one way or another would need to be registered in Indiana.
Being you have an entity registered in Illinois, you could use that as a holding company, which would own a company in Indiana that in turn is holding the property. This would make sense if you want to further separate your personal assets from the property by having an additional layer of liability protection. If you are a resident of Illinois state and were planning on writing-off your business expenses, then it would likely make more sense to register an Indiana LLC, owned by your IL LLC.
Keep in mind, if you would be living and owning a property in Indiana, then it may make more sense to dissolve the Illinois company and just register a new LLC in Indiana.