OK, so now that I've seen the clarification...
Having travelled through a lot of these countries, let's just go with the list of them:
Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland.
That's 25 countries in the Schengen Area.
Given you're concerned about accommodation, I'll focus on hostels. Most do offer one or two double rooms as well as the dorms, so you can stil have your privacy at a low cost. However, generally the same rules will apply to other more expensive forms of accommodation.
Now, accommodation varies, but that's not the total cost of the trip to a place - in some places it's a small part. But we'll focus on accommodation for your question.
Numbeo.com gives a guide by having the average cost of living for a bunch of countries, and breaks it down by rent. Generally, this can be used as a guide for hotel/hostel/accommodation rates. Again, however, this varies depending on what type of accommodation you're prepared or want to take.
Livinginahostel.com has an article (from a year ago) about the Top 10 Most expensive countries to stay in a hostel in Europe. Top lesson from this list - Scandinavia is brutal on the wallet! I can confirm this. From this list, you can probably knock off Norway, Switzerland, Luxembourg, Finland, Denmark, Iceland, Sweden. The others aren't Schengen.
So now we're down to Austria, Belgium, Czech Republic, Estonia, France, Germany, Greece, Hungary, Italy, Latvia, Lithuania, Malta, Netherlands, Poland, Portugal, Slovakia, Slovenia, Spain - 19 countries.
From personal experience - again, it depends on the city, the hostel and the time of year, quite often. Where I've been amazed at the low price, it'd be parts of Spain, definitely Poland (Greg and Tom's hostel in Krakow is one of the best I've stayed in and the cheapest), and Lithuania and Latvia too.
Fortunately, we have yet another list to help out with this - the 10 Cheapest Countries for Hostels in Europe. Again there are some on this list that aren't Schengen, but of the ones that are, it includes Poland, Germany, Latvia, Hungary, Estonia, and Czech Republic.
I personally raise an eyebrow at the Czech Republic and Estonia being on there - since the Euro, Estonia has gone up a bit, but perhaps it just felt more expensive after Lithuania and Latvia. The Czech Republic may have low price accommodation, but other stuff wasn't that cheap from memory. Although we did eat well. Germany too, has price increases over summer, and certainly Munich prices rocket for Oktoberfest!
If you do use Hostels, it pays to check on hostelbookers and I recommend Booking.com for non-hostel. AirBnB is also being mentioned regularly of late, but I've not used it myself.
Good luck and have fun!