A man advertised to have storage for his car for the winter (it snows here!). I have the room in my large garage. He does not know what to pay me. I don't know the going rate, or what I should charge, would you be able to help me with that?

I live in the Midwest...

I'd say the very least you should charge is $50.00 to $65.00 a month.

Here is a page that might give you an idea of going about it
Reading A Garage Rental Agreement Carefully

Is he going to have to access the car daily, will have have a key and ability to get into your garage without anyone else there.

Also is this downtown NY or rual Tennesse. In NY several hundred dollars would not be out of line, in rual TN around 50 to 75 a month

I would check into storage sites such as U-Haul and see what they charge. Additionally you may not want to let him have access to your garage if you don't know him well. You could be liable for any damage to his car while it is being stored in your garage.