I had the pleasure of being in town during the Broadway tour of Book of Mormon at the KeyBank Theater in Playhouse Square. The whole area is lit with an actual giant chandelier, lights and excitement.
There were a lot of people out and about for a Wednesday night! The KeyBank theater is great, very big and spacious- a rarity for those who are used to attending shows in NYC! The production was fabulous, I sat in the center mezzanine and had a great view of the stage. The lines for drinks/snacks were not long and both the tickets and food were very reasonably priced!
The whole area had a lot going on so i suggest if you're in downtown Cleveland I would suggest looking into the Playhouse Square events calendar- you'll probably find a really great time!