Where are the best places to entertain kids in Cincinnati?

That depends on how old the kids are.
Gynboree is great for little kids. My daughter has my 1 year old grandson enrolled for a Mommy and Me class.

I take my 4 year old to the Museum Center. For whatever reason, he gets a kick out of the mini Kroger store. He also likes the ball area where they toss balls, have them sucked up by a vacuum and blown in the air. (You have to be there)

We actually had the 1 year old's birthday at the Museum Center. They had a private room, two staff members and they got a chance to touch a snake and a turtle. Speaking of animals, the Zoo is pretty nice for kids old enough to relate to animals.

El Porvenir grocery store is located in Mt. Carmel--it's small and lively with a great deli. For something more accessible, check out La Mexicana in Newport, KY. This store is similar to El Porvenir but much more accessible to those who don't live near Eastgate.

I personally recommend the Cincinnati Museum Center's Children's Museum. I take my 7-year-old sister there on occasion, and she is entertained for hours. It takes up an entire floor of the museum and is a lot of fun for both children and adults. In addition, you can stop by the Omnimax theatre and see one of their famous IMAX films afterward--kids love those!

If you're looking for something outdoors, though, I recommend the Cincinnati Nature Center. They have classes and camps perfect for kids who enjoy the outdoors. It's a great way to get kids out and about while learning at the same time.