Hi there,
Glad you like the website.
Hotel accommodation in Sydney, or any short term accommodation for that matter, is not cheap.
I understand your reservations about backpacker places. But you may want to consider the YHA at Central Station.
You could try the YWCA. Their website is
http://www.yhotel.com.au/ They offer backpacker type accommodation and single rooms. The City South Y is in a noisey spot, so I'd go for the Hyde Park one.
Or you can try Unilodge. They usually charge $130 a night but have cheaper rates for longer term bookings. It's in a very convenient location with plenty of shops and transport literally at the door.
http://www.unilodgehotel.com.au/sydney/I'm not sure about budget accommodation in Ryde.
Enjoy the move. You'll like Sydney. There is always so much to do.