For a family trip, I can personally vouch for the Salisbury YMCA hotel in TST, Kowloon side. Nice rooms, not fancy, but nice, good view, right by the Peninsula, great rates and service. It is a full service hotel, not the YMCA stereotype that might first pop into your mind. Try to get a rate that includes the breakfast buffet (International cuisine, heavy on Western items). It is very good.

I book nearly 100% of my Asia hotel rooms via asiarooms.com. I also recommend agoda.com and hotelclub.net. I find that Asiarooms.com beats the socks off of Expedia, Orbitz and Travelocity, etc. I have 2 HKG stays booked in November and December, one in Singapore and 2 in Bangkok booked through Asia rooms, as well as many previous trips. Nothing has ever fallen through the cracks on any of my reservations.

Good luck, and I hope you enjoy HKG as much as I do. It is my top destination on the planet.