God, where to start! Singapore is a great city.
Sentosa is great for kids and a nice break from the biz of the city. It's easy to get to. My favourite way to do Sentosa is to get a taxi to Mount Faber. Enjoy the green leafyness more in keeping with Singapore of days gone by and get the cable cars across to Sentosa - great fun.
At the top of Sentosa there are several things for the kids - just google. Then take the Luge (go carts) down to the beach where there are some nice chill out beach bars for a drink or some lunch - People aren't always keen on the sea for swimming but not sure how safe the water actually is but the kids will enjoy playing in the sand and paddling. Of course you also have Universal Studios (just remember how hot it gets and jet lag) and a Water park. You can catch the monorail back across to Vivocity City, a lovely shopping mall with cinemas, foods courts, cinema, playground and splash area for the kids.
Sentosa would be more peaceful but you have lankawi for that. You could stay more central so you can walk and be in the biz more.
Singapore zoo is fantastic, best I've seen and cheap compared to similar attractions in the UK. It has a great play area and water park for the kids.
Botanic gardens at the top of Orchard Road is lovely for breakfast and a stroll before hitting Orchard Road if you fancy some shopping. It also has a special children's garden with hands on stuff and some play based things.
The river is nice to walk along down to the bay to see the Merlion. You can go to the Skydeck at the Marina Bay Sands Hotel for an amazing view of the city. Chinatown is probably better to visit at night. Lots of cheap little shops and you can eat fairly cheaply.
The East Coast Park is lovely if you want to go for a bike ride and catch some lunch. It stretches miles along the coast and the hundreds of ships moored just off the coast is a sight to see.
Eating can be very expensive in Singapore (and drink). You can eat very cheaply though if you go to food courts and pick little cheap cafes - usually plastic talbles and chairs but the food is great and cheap and fun.