My personal preference is to stay in Kowloon area.
As budget is an issue,
$150 range, I suggest BP international
(3mins walk fr Jordan MTR)
$100 range, I suggest Sing Ho hotel
(Great location, stone-throw away from Mongkok shopping district)
$100 and below [not recommended for single ladies, couple still fine]
(Hotels with hourly rates, daily rates available. Sleazy but still clean and safe. Best of all, its much spacious than any hotel within this budget. Along Temple St or Mongkok)
If your preference is to stay in Hong Kong Island, be prepared to pay slightly more...