Glidden House is close to the Art Museum, Botanical Gardens, and Case Western (it's probably the closest, cheapest option). I really enjoyed the setting and found the staff super friendly and helpful. Some previous reviews complained about the breakfast. I thought it was pretty good with plenty of protein options (boiled eggs, sausage, yogurt). They didn't have an omelet chef or anything like that, and options were a bit limited - but I only paid $169 a night (which isn't really enough to justify asking for a robust breakfast). That said, you could stuff yourself with good food at their small buffet.
The rooms and interior itself is well done and it was a welcome change from chain hotels with the same boring furniture. I felt like my room and bathroom were recently re-done as everything looked new. The temperature in the room was always pleasant, and the only complaint I had was I wish they had a small fridge in the room to store some food (particularly leftovers from eating in Little Italy, which is a short ten minute walk away). I did not eat at their restaurant, so cannot comment on it. But I did go to the Barking Spider Tavern just behind the hotel and it was great.
I would definitely stay here again next time I'm in Cleveland.