The recommendations here so far (spanning from Chungking Mansions
to the Eaton Hotel) are pretty broad... perhaps a clearer definition of
how "cheap" you are looking for would help...

One other point of information for you... When I travel to HK, I would
not dream of going as "downscale" as Chungking Mansions, but I also
would consider the Eaton or the Salisbury YMCA to be a splurge. For
my budget, I usually like the Evergreen Hotel (www.evergreenhotel.com).
Nice location, clean and quiet rooms, close to transit and the airport
bus stop.

Just one more to consider.