It will probably be difficult to find a room for four people for that price. Especially for a room with a harbor view . . . during holiday season!
The following is a budget hotel in the Kowloon/Tsim Sha Tsui area. It's a couple of blocks away from the Temple Street Night Market. Walking distance to Jordan Station and Kowloon Park. It has no view at all!
However, you can get a room with four twin beds (so everyone sleeps well!) that includes breakfast, computer access (with internet), free washer/dryer, onsite travel assistance, etc. It's a family run place. My husband, two children and I have stayed there for the past four years when we travel to Hong Kong for Chinese New Year.
It's the Evergreen Hotel, on Woo Sung Street, off of Nathan Road. You can read about them at
http://www.evergreenhotel.com
They don't advertise their four-bed room anymore, but it shows up on the reservation pages. Or, you could call them. It's $950 HK per night (that's $122 US).
Good luck!