Well, Singapore, the newest and most popular attraction would be Marina Bay Sands and the Casino. I like going to Bugis for a bazaar/flea market experience. For a seafood experience, you may visit the Esplanade. Travelling by public transport is convenient in Singapore.
I’m from KL, I guess the popular tourist attractions would be Suria KLCC (Kuala Lumpur City Centre), Bukit Bintang/Bintang Walk, MidValley Megamall. There are not many Malaysian grown beauty or fashion brands; most brands are UK or US, or even Australian. There is Sephora at Suria KLCC. Batik is a Malaysian/Indonesian traditional printed fabric, so you may want to buy some of that. A noted designer that uses batik in his designs is Eric Tho; you will find his boutique at MidValley Megamall. Pewter ware is famous in Malaysia; we used to be largest exporter of pewter. You may want to visit a Royal Selangor Pewter store (I believe MidValley Megamall has one) to look at pewter ware.
For more information on Malaysian famous designers and where their galleries are located go to http://www.kuala-lumpur.ws/magazine/fashion-guide.htm
You may want to visit Chinatown at Petaling Street; although, personally, it has lost its quaint charm since it has been re-vamped (probably about 10 years ago).
Just outside of KL is a popular tourist attraction called Batu Caves, limestone caves with an Indian temple built inside of the caves.
By contrast, travelling by public transport in KL and Penang is not as convenient. If you do travel around, you could get a taxi, make sure you request for a metered taxi, and that the taxi driver uses the meter.
Penang has undergone major transformation over the last 5 years such that it is tourist-friendly. Several Chinese temples (Kek Lok Si, Snake temple) remain the popular tourist attraction, Penang Hill, seafood is abundant in Penang, you may want to visit Gurney Drive, Bukit Tambun, and Batu Ferringhi. Penang Laksa (Ayer Itam) and Char Kuey Teow (Lorong Selamat) is a must-have in Penang; ask the locals!
If you need more information, let me know!