I have stayed in a number of hotels in HK but all for work and so, like Janus, I can't comment on their child friendliness (I would say though that generally in HK children are pretty much welcome everywhere).
I have stayed at both the Marriott and the Hyatt. They are both on the Island side and both central. On balance though I would say that the Marriott has the better location being close to the park and a 15 minute walk to the Star Ferry. One hotel I wouldn't recommend is the Ritz Carlton (very expensive and prissy). Both the Marriot and the Hyatt are very nice with good sized rooms and all the amenities you would expect. The Hyatt is definitely the nicer of the 2 but I would suspect it is considerably more expensive. I usually stay in the Mandarin but I wouldn't recommend it for children.
If your budget can stretch to it, I would really recommend the Island Shagri La. It has the nicest and largest swimming pool I have seen in HK and is a very glam hotel all round with very nice staff. All the rooms are good sized and most have great views. It is also adjacent to the park and again, a very manageable walk to the Star Ferry and Central (or a ridiculously cheap cab ride).
If you want to stay in Kowloon, I would recommend the Regent. If all of these are too expensive, you might try the Excelsior which is also on the Island and (I think) is 4 rather than 5 star.
A word of warning though, even if the room rates appear reasonable be prepared for pricey food within any of these hotels. Room service is a killer!