Wow!! These are tremendous rates for some very good hotels.
You do not need be afraid of the Gran Via, and the Cibeles should be just fine. It is a very vibrant street, and you and your daughter will feel comfortable.
I wouldn't rule out the Atocha either. It was completely re-done a couple of years ago, so it should be nice. The location of the Ambassador seems good too.
Have a good trip. And if you are a Starbucks fan, there is one on the Gran Via at Callao, which is not far from the Cibeles.