Not sure what's your budget but basically there are two options:
1. Nice posh hotel or 2. Family based apartment type
I have stayed in both. and the following are good to start your research..
1:CHI Residences 279 279 Shanghai Street, Yau Ma Tei
We stayed there with two kids and two adults... not too pricy and located about 5 mins from Yau Tei MRT... along Yau Tei is also where your Ladies' Market, Sports Street are located... below the apartment you have the Hui Lau Shan ;the most popular and famous healthy dessert restaurant in Hong Kong.. Opposite the hotel you have loads of food stalls.. one in particular at the corner is a Teochew Tze char.. the food is super cheap and super nice... tons of roast meat shop etc...
We took MRT with kids on tow to shopping areas like Causeway bay, Times Sq, Harbour city.. easily... (Avoid peak hours though)
2.Langham Place Hong Kong 555 Shanghai Street Mongkok Kowloon, Hong Kong, Hong Kong
Posh place right at the top of a big shopping centre.. almost perfect location cos you are in the heart of shopping, dining, and entertainment. Other local attractions include the Ladies Market, the Night Market, the Hong Kong Convention and Exhibition Center, the Jade Market, Mongkok, Victoria Harbor, and the Fish Market. We also went with 2 kids... and pram... we stayed there and went to Disneyland instead of Disney hotel (ex) ..downstairs you have nice restaurant, HK cafe, and local oldies tea houses, breakfast places, wet market... i love it