The first time we traveled with our baby boy was when he was four months old. I had just relocated to Singapore a few months earlier and my wife and son where coming over to finally join me.
Singapore has a sterling reputation as a very child friendly place to visit. And this reputation is very well deserved. From being very clean to having a very low crime rate, Singapore is a fantastic destination when traveling with small children.
Transportation
Taxis - Easiest way to get around. Singapore taxis are clean and efficient. Most drivers are friendly and speak English. Lots of clearly identified taxi stands and you can flag down a taxi in most places in the city except along major roads (like Orchard).
Trains - Clean and efficient. All stations are equipped with lifts to get from the street level to the platform. This is very important for those traveling with prams. Also, most stations have safety doors that separate the trains from the platform. The trains also stops leveled with the platform so there no need to lift prams over an elevated area when getting on and off the train.
Buses - Again clean and efficient. Sometimes they can get a bit crammed but adults generally will give up their seat to a mother traveling with a baby or small child. You can also ask the driver to notify you of when you reach your intended stop in case you are unfamiliar with the area you are traveling to.
Places of interest
Singapore Botanic Gardens - Our favorite place to visit during weekends. Most of the park can be accessed free of charge. It's a great place to bring small children as they can run around and play. They have areas where families can lay down a blanket, relax, play catch or read a book.
For more info you can visit: http://www.sbg.org.sg
Singapore Zoo - Great place to visit. It's a zoo, lots of fantastic animals and animal shows. Need I say more?
For more info you can visit: http://www.zoo.com.sg
Night Safari - Something for bigger kids as smaller kids might not be able to appreciate seeing animals at night. Still, a great place to visit. The park has clearly identified paths so there is no fear of getting lost when you and your kids explore beyond the popular Tram Ride.
For more info you can visit: http://www.nightsafari.com.sg
Malls - Singapore has loads of shopping malls. One that particularly stood out to us was Forum: The Shopping Mall along Orchard as they had a lot of children's specialty clothes brands as well as a Toys R Us. It's not the biggest or most popular mall but it's a good place for parents to shop for their kids.
Other more popular malls: Vivo City (they've got a big play area for kids), Ion Orchard (connected to a host of other malls via underground tunnel, perfect when it's raining or too sunny outside), Marina Square, 313 Somerset (connected to the MRT station for easy access).
Science Centre Singapore - For fun that's educational too. Even parents should enjoy this one! They regularly have special exhibitions (currently Dinosaurs Live until February 2012) that change every season and an Omni Theater (IMAX) to boot.
For more info visit: http://science.edu.sg
Singapore might be small but this island is a great place to visit with your kids. There are loads of things to do and places to visit (I haven't even touched on Sentosa). There are also a lot of pocket parks (Fort Canning, Mt Faber, Chinese Garden) to visit where one can spend a relaxing day strolling with your kids.
People in Singapore are generally friendly and even more accommodating to those who travel with kids. As Singapore is the hub to Southeast Asia, it's a melting pot of cultures and people. There are all kinds of international, regional and local cuisines to try and it's a great jump-off point to visit other parts of the region.