How important is the private room? Following is not a recommendation - I do not vouch for this property but mention it because I saw an article about this hostel written up in the Today newspaper: The Adler Hostel, started and run by Adler Poh. Also included is a link to a travel agent newsletter, TTG Asia.

http://www.todayonline.com/Singapore...nd-hes-only-25

http://www.adlerhostel.com/#

http://ttgasia.com/article.php?article_id=20193

I'm suggesting this is worth a look mainly because it's new, so too early for the place to have gotten all beaten up and worn out, the photos in their website seem to show a decent place and the articles make it clear it's not a love hotel. Most of all, it looks like it fits all your other criteria - both key ones, and nice to have.