I think the cheapest is likely to be Ibis.
Go to http://www.accor.com. The problem is, just looking now, is that all their Stockholm hotels seem to be in the suburbs. When I looked at that site, I also saw something called Formule 1 hotels, which seem to be even cheaper, but I think they are also in the suburbs. Be sure to check if Formule 1 has private baths if you go with them. http://www.hotelformule1.com

I am staying at Ibis in Goteborg and Malmo, but the locations of those are not so far out. You are unlikely to do better than Ibis for a cheaper price, particularly if you want a hotel with a private bath. I asked about this chain on USENET, and several posters assured me the hotels are clean and of a good standard - a cut above Motel 6. They are run by the same French company that runs Sofitel, Motel 6, etc..

Have you looked at TravelAxe - http://www.travelaxe.com? That's a good site for finding cheap hotels. If you are willing to give up a private bathroom, look at Rick Steeves' Scandinavia book for some tips.

[This message has been edited by WillTravel (edited 06-01-2003).]