Luckily, based on reviews that I found at cleveland.com, I believe that I will instead have the opportunity to eat locally sourced food at Pura Vida or the Greenhouse Tavern (GHT). The first apparently specializes in American Cuisine and is located on Public Square, while the second specializes in French Cuisine and is located in the E. 4th St. district. Both Pura Vida and GHT believe in providing vegan/vegetarian options. While I am not vegan/vegetarian, I like fresh local food and that often comes with the territory. So I might actually check out the vegan deli/cafe Flaming Ice on Public Square while I am in Cleveland.
Finally, some other happy hour options recommended by cleveland.com (besides Pura Vida and GHT) might be Bar Louie in the warehouse district or Pickwick & Frolic (yes named for Dickens' novel) in the E. 4th St. district.
To keep this data together so that I do not have to look it all up again, I have put together a google map with these interesting restaurants on it.