Accommodation search engine that allows setting an approximate price range without a date?

While looking for accommodation for my vacation, I have become rather frustrated with sites like booking.com where you have to set the check-in and check-out dates before you see any prices. Unfortunately I am at a (probably not unique) position where my schedule and destination preference are not by any means tight, but my budget is.

Are there any accommodation search engines that allow you to set a destination and an approximate price range without an exact date?

EDIT:

Let's rephrase this question in another way:

Is there a site that would show a "From X Euro/$ per night"-style price tag when supplied with an area and a date-range? Normally From-style price tags are a major problem, but in this case they could help a traveller weed out places that are too expensive and track down potentially good deals.