It's named after a steak, so it has to be good!
I've been to Delmonicos three times so far (2 for business and 1 for a personal occasion) and it's been a positive experience each time. As others have mentioned, it is a higher end establishment so try and look nice.
The bar area is relatively large and you can wine and dine there if you prefer. I start out, go with, and finish with Ketel One on the rocks. This place serves bleu cheese olives in bunches (three to be exact).
I've never had their namesake, the bone-in Delmonico, but another guest did. It came out a little undercooked in parts and a little fatty, but that is almost expected with a bone-in steak. I've had strip steaks and filet mignon and have been content. Is there better steak houses in Cleveland? Probably a couple, but Delmonico's is probably the lesser expensive of the options.
The last visit (the personal one) didn't go as smoothly as the others (waiter underprepared and he under delivered, steaks weren't cooked exactly as requested) but I've been satisfied each time I was there. They typically assign two waiters to a table as well.