The hype is real!
I've been here four or five times, and never felt bothered to review it due to the sheer volume of reviews already submitted. Echoing what others have said, what do I have to add? LeBron James is good at basketball, Austin Texas is hip, there's a drought in California, and the Greenhouse Tavern makes good food, yada yada.
But, browsing recent reviews and seeing a flurry of whiny accusations of overratedness and angry 1-star tantrums over a single bad experience, I feel the need to say something.
As a said, I've been here four of five times, and sure, there was an off night sandwiched in those visits, and a few items that missed their mark. But please - to condemn an establishment based on an occasional shortcoming reminds me of the American who spends two nights in Paris on a guided tour, and then announces to his or her friends at home that the entire country of France sucks and that the French are awful. The Greenhouse is Paris; it has a great reputation that is well-earned, but remember that Paris still has ghettos, mean people, traffic and bad food.
Anyway, here's my schtick: there's a bar on the right when you walk in that is staffed by very knowledgable bar people who execute their drinks perfectly, and seem proud to be working on the cutting edge of gastronomic culture. They will talk the Cleveland food scene with you, tell you what to order, and tell you where to go next. You'll get everything you need here in the bar; don't bother with the restaurant part, and certainly don't book your 20-person birthday party here. The finer things in life are enjoyed in small, intimate, concentrated doses.
The food is all about the wings; everything else flows from there. Simply describing them as "the best chicken wings ever" won't do. To give you a better idea, they are good because they undergo a slow, low-temp oven-roast that allows the wings to cook in their own rendered fat. This "confit" method is almost always though of as a duck thing, but as a chicken thing, it shines and delights. There is no sauciness about the wings, either. That would take too much attention away from the perfectly cooked meat. Instead they are tossed in a little lime juice, fresh cilantro, and minced garlic (I think), to add a fresh and tangy accent. These wings are so succulent and thoroughly roasted that you can actually eat the bones.
Lobster in Maine, salmon in Seattle, barbecue in Memphis, confit wings in Cleveland. That's the territory you are entering into here. Ride this wing high into the rest of the menu, and let me know what else you find; I haven't gotten that far very often.