Here's an early ad (below) for the pair of restaurants that ran in the 1973 Lorain Telephone Book. The identical ad ran in the Elyria phone book.
Although the Lorain restaurant disappeared from the phone book and directory in the early 1980s, the Elyria location apparently thrived, lasting into the 1990s. It too was absent from the phone book by 1996.
I never had the chance to eat at either Tiffany's location, which is too bad.
I think the place was ahead of its time. It looks like its steakhouse theme would really be a winner now, with manly meat fare and old school cocktails regaining popularity.
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I think this same building – with a 4900 West Erie Avenue address – was one of the homes of Ed Blahay Transportation Company, and later, Benny's Restaurant. I'm going to have to do some more research and confirm it, and then prepare a proper post in the future if that's the case.