So, a bit of digging shows that this isn't a new question.
It's been asked in several places around the Internet.
One notable example is a site called MightyTravels, which, in an article about this exact problem, makes an interesting claim at the bottom:
Did you know – with Mighty Travels Premium you can search 365 days of hotel rates sorted by deal price or savings off the average rate. We cover 20,000 different properties.
However, their page about their premium service makes no reference to this feature. Therefore the above quote seems likely to either be a lie, or a now discontinued feature.
I can find various persons claiming that Kayak does (or at least used to) offer this functionality. However I cannot find it now. TripAdvisor SuperSearch's google description claims it offers this, but again, no sign of it on the actual site.
I have however found two actual, meta-search possibilities:
- Hotels Combined - there is a check box on the search page saying "I don't have specific dates yet". When you perform a search like this, it seems to work, providing a list of hotels with their cheapest 1-night rates. However, clicking through to find the actual dates they are offered, instead shows you the prices for the last dates you searched with (or the default dates if you didn't)
- Booking.com doesn't explicitly provide this, but it does (sometimes?) try to help you out, by suggesting other dates with cheaper available rates. The box sometimes pops up in the sidebar, sometimes at the top and looks like this:
Finally, in addition to the IHG and Hilton options offered above, the Marriott chain offers probably the best option of the lot. Go to their site, enter a location (approximately), click the dates box, then hit flexible dates when the box comes up. Enter the number of days (doesn't seem to offer flexibility there), then pick an individual hotel. You know get a month-long view of prices for stays beginning on every date, and can easily step backward or forward a month.