Hauz Khas is one of the hidden gems of Delhi but I won't say it's a perfect place for your kids. At Hauz Khas more than kids you will find young couples and college kids.
What's there for kids... At one side you will find deer park and on the other fort with big garden and lake. Kids enjoy looking at Deer,rabbits ,chicks, peacocks and birds. And they love to run and play in the garden with their parents or same age kids. But this fun can be done only on a cool day or in winters. Hauz Khas it's definitely not a place to go in summers because your kids will not be able to beat the heat. There are lots of restaurants but mostly are with pubs and kids are not allowed . Still fooding will not be a problem because it's all hygienic food in the kids allowed restaurants and the washrooms are also neat .
There are many shops,boutiques for shopping but all are over priced and heavy for your pocket. It's better to leave this place by night if you are with kids... Because you will find many drunked people around.
You can take your kids stroller but it's not accessible in the fort. Don't forget to take sheets and toys like ball along with you.
Overall it's a nice place to spend a winter afternoon.