Accommodation websites

Does anyone know of an accommodation booking website where you can search by the hotel/city to find the cheapest price it is available at over any given period?

Rather than go away for a couple weeks this summer I'm thinking about for the next seven or 8 months I'm going to just go away a number of times to different European cities for 2,3 or 4 days using budget airlines.

Now I have no specific dates and I'm very flexible so would like  to just find a time when a city has the cheapest accommodation available and book when I can get best value for money when flights are available. The problem is most of these accommodation search engines want you to put in specific dates to search or when you search for hotels or a city and and get  'from price' they ask you to put in dates to confirm prices.

Does anyone know of a site where for instance you could search for accommodation based on for instance the cheapest time of the year in dublin for 3 or 4 star hotels like you can do on Sky Scanner and other airline sites where you can check the cheapest price per month for a particular route?