Since this was posted on the CC forum, I assume that the OP is looking at CC hotels.
1. Input your city on the CC website
2. Input a month range for check-in/out. For example, checking in on Aug 6 and out in Sept. 5
3. Input your particulars (Number of guests, number of rooms, etc.)
4. Search
See the rate listed? Underneath it is something that says "Rate details" If you click on that, you get a calendar of every rate within your search criteria. Now your know what dates are the cheapest.
It's not 100% because some hotels will give you a discount for multi nights. However, while the rate may increase a bit, the cheapest rates will be on the same nights. I used this religiously for the recent promos.