Most hotels have a "day rate" that is less than the regular (overnight) rate. However, you usually have to check in during the morning and check out by 3:00pm to get the Day Rate.
I don't know of any legitimate hotels that charge by the hour.
You won't find an hourly rate hotels here, there are none. There are some hourly motels scattered around the city, like on Metropolitan Ave and Mermorial Drive.
There are a few on Fulton Industrial Blvd. It is one of the seediest areas in Atlanta, though. Drugs, prostitution, and other sorts of crime are everywhere there, and the hotels on FIB cater to that "market". I would proceed with caution.