Singapore and Malaysia offer plenty of options but I assume child-friendly activities will be a priority for you. I am also assuming that you will divide your time equally between the two places.
Just 20 minutes’ drive from Kuala Lumpur (KL) is the Bandar Sunway township, home to Malaysia’s premier theme park, Sunway Lagoon.With a 9-year-old in tow, you can spend a day exploring the Sunway’s amusement park (Pirate’s Revenge, City of Gold Scream Coaster, Captain Kids’ Playland and Candyland, etc.) water park (Waters of Africa, Waterplexx 5D, etc.) and the interactive wildlife park. You can stay at the Sunway Hotel Resort and Spa; check their website (http://kualalumpur.sunwayhotels.com/) for family packages.For shopping, you can visit the adjoining Pyramid Shopping Mall. Sunway now provides free shuttle bus service around Sunway Resort City. You can stay in Kuala Lumpur too; depending on where you are staying, you can take the train to Subang Jaya or the Kelana Jaya stations, and then the feeder bus to the Sunway Pyramid stop (5 minutes from the theme park).
Although famous for its casinos, Genting Highlands, an hour’s drive from KL, is an integrated tourist center with theme parks, hotels and other attractions; most of these are connected through a maze of walkways and passages, making it relatively easy to cover the entire place in a short time; you can take the Genting Skyway (cable car), from the foothill town of Gohtong Jaya, to reach the peak. But note, owing to redevelopment of the area, a few rides in the theme park will remain closed during your time of visit. You can spend a day here or stay overnight.
The best way to sightsee in KL is to avail The KL Hop-on Hop-Off Tour (9am to 8pm); plenty of options to choose from. The double-decker, air-conditioned bus covers 22 designated stops and over 40 attractions. Details available on http://www.myhoponhopoff.com. Some of the must see attractions of KL are the 88-storey Petronas Twin Towers (closed on Mondays; buy tickets online to visit the mid-level sky bridge, https://eticket.petronastwintowers.com.my), Perdana Botanical Garden, KL Bird Park (especially during the bird feeding time) and Zoo Negara; Batu Caves, 13km from KL, is a Hindu shrine; you have to ascend more than 250 steps to reach the temple; most stop en route at the Selangor Pewter Factory.Shopping malls are aplenty in KL.
Or, after an overnight stay in Bandar Sunway, you can fly directly to Langkawi from KL for a two day trip; Langkawi is known for its picture perfect beaches and duty free shopping. In that case, I suggest you drop the botanical garden, the bird park and the zoo from the KL itinerary as you can visit similar attractions in Singapore.
You can travel between KL and Singapore by road (4 hours) and rail (6-7 hours). One more point, Singapore is a little more expensive than Malaysia.
There are plenty of things-to-do in Singapore. You cannot miss the Singapore Zoo, the Night Safari,the Jurong Bird Park andthe River Safari. The zoo’s Kidzranger Tour (for 5- to 12-year-olds, $15) allows children to become zookeepers during the tour; with their special vest and a pin-on button, the kids get special access to areas in the Rainforest Kidzworld that are otherwise only open to the real zookeepers. The Singapore Attractions Express Bus Service (www.saex.com.sg) is convenient for travelling to and from the attractions in Singapore as well as for visiting Sentosa Island.
Sentosa, the popular island resort, is just 30 minutes away from Singapore city; this island of ‘endless attractions’ can be reached by bus, train and cable car. The attractions have been grouped under Siloso Point, Imbiah Lookout and Resorts World Sentosa (which includes the Universal Studios). The island’s 3.2km long beach is also a popular attraction. The Universal Studios consists of 24 movie-themed rides and attractions.
Visit the famous shopping street of Singapore city – Orchard Road. Chinatown and Mustafa Centre (in Little India) are good for souvenir shopping.
Also, always remember to check the websites of the individual attractions for concessions and special packages; some even offer web-exclusive discounts.