Dilinger's

[ronbutters at AOL.COM]

Wrong. There is a restrictive relative clause (you just don't see it because the "which is" was deleted):

"Dillinger's sometimes hands out fliers at Broad and High streets reminding people [that] the restaurant, which is on the 16th floor of the LeVeque Tower, has a patio just for smokers."

I suppose in theory the referant could be some unnamed restaurant other than Dillard's, but in that case we would expect "a" to go with the restrictive relative clause (unless a sentence named the other restaurant and preceded "Dillinger's").
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