I would recommend Moxie.
I also like fire and Dante, but judging based on consistency I would pick Moxie over any of the restaurants mentioned above. Moxie's soups, fish and sides are all executed with a higher rate of success. Also, Moxie is only one of two restaurants in Cleveland where I've had good chicken in the past five years. (If you're looking for red meat, I'd recommend the flat iron over the burger, filet or strip.) Moxie is a little further out of the way and the neighborhood lacks the charm of Ohio City or Shaker Square. The food at Moxie is also (I had a very hard time finding the right way to describe it and I'm not sure I succeeded) conservative. That doesn't mean it's boring. There are daily soup and fishes specials and frequently also appetizer and entree specials. The regular menu changes frequently, too. I think they feel somewhat constrained by an unadventurous clientele, but they work very hard to offer a good variety and keep their menu interesting. And conservative or not, the flavors are as good as any restaurant and definitely the most consistent in Cleveland. That's why I'm there almost every week.
In addition to fire, Dante and Moxie, I'd also recommend Sapore, Bar Cento and the Flying Fig. Sapore is even further east than Moxie but it's still ~35min from downtown. The Fig and Bar Cento are two more restaurants in Ohio City. The Fig's meals start with the best bread service in the city. Frankly, it's a welcome respite from what, in so many places, seems like an afterthought. Bar Cento has fantastic french fries. The food is simple food that's usually cooked well from ingredients that you can feel good about. Actually, the Fig, Sapore and fire are all also very conscientious about sourcing ingredients.
So many great options. A really great and growing restaurant scene. Three distinct areas to consider: Tremont/Ohio City (west of the river); East 4th Street (downtown near arenas/stadiums); Shaker Square area (east of the river).
In Tremont/Ohio City, consider Lolita's (Michael Symon's first owned restaurant, renamed but still run by Symon), Parallax, Dante's, Fahrenheit.
In East 4th area, consider Saigon, Greenhouse Tavern, Lola (Symon's original name, new location - good luck getting reservations), Chinato (just opened, so can't comment on food)
In Shaker Square area, there is Fire, Sarava, Felice (on Larchmere).
Enjoy the hidden gems!