There is a hostel just off rue de Lausanne which is around that price.  Often used by foreigners overnighting in Geneva but I think it is dormitory accommodation.  It is clearly advertised on the wall of Cornavin train station.  If you come out of the station with the ticket office on your left then it is on the wall to the left of the exit door.

Maybe somebody reading this answer will be able to give more details, otherwise just pop down to Cornavin.   I hears about it while talking to someone at the airport and then found the sign immediately in the station.  Have no idea how good or clean it is but cannot be that bad otherwise poeple would not be recommending it.  

Also these places often have double rooms at slightly higher price.  

CareenaPaul - thanks!!

careena - I've Googled all 3 options you've given me : 1 isn't available, one looks somehwat shabby and the third doesn't have any pictures of the rooms..

Paul: I've searched for "rue de lausanne" and there are way too many options... could you narrow it down to the name of the hostel itself?

From a quick search on google, I have found a cheap option (http://www.hihostels.com/dba/hostels-Geneva-055035.en.htm) though I have

no idea how recommended it really IS

Any furtherother suggestions would be gladly welcome :)

I thing the hostel Paul was talking about is the City Hostel. I guess you've googled that one.

The terms "cheap" and "midst of Geneva" are not compatible with each other...

The one you found on hihostels is the Youth Hostel (Auberge de Jeunesse). On their website they say that they're partially in renovation so don't know how many rooms they've got right now...

The Home St Pierre is kind of a special place - as you might have noticed from their website. They're primarily a student home for women, but offer dorms also for men. The location is beautiful, right next to the cathedral.

That's about it for cheap places, but you can always check out hostelworld.com.

I've never been inside any of the hostels but don't worry, hostels in Switzerland are usually clean and ok.

Ever thought of couchsurfing.org?

Eva

Yep, I have Googled City Hostel (http://www.cityhostel.ch/english/) and they dont have any vacancy, strangely enough..

The term cheap and Switzerland is paradoxic, I know :|

"Home St Pierre" don't advertise their prices.. I've emailed them regarding the matter.

I've checked out hostelworld.com... 

CouchSurfing isn't for me... I'd really like my privacy, honestly..

Thanks!!!!!!!!!!

Any other insights, anyone?
I'm not necessarily looking for a hostel smack in the middle of Geneva... I could travel by bus or train.. might even rent a car or smtg 

Thanks in advance! :)

Found a few options on http://www.hostelbookers.com/ but am still undecided :|