A few points to note:
A lot of the stuff/fabric you see around is made in China. I don't think they are quilt-suitable. You don't want those.
Quilting is not real big in Singapore. There is a Australian chain called Spotliight, kind of like Joann's. But you are much better (variety and price wise) with Joann's.
The batik you see in Singapore or Malaysia is slightly different from the ones we are used to (for quilting). The common batik there is worn by Malay ladies as skirts/sarongs. They have intricate designs and are pure cotton as well. I bought a couple of them. I even made a quilt out of it.
If you want to have a look at batik fabric, you can look around Arab Street (fabric heaven, though mostly for dressmaking, be prepared to bargain), Geylang Serai (Malay enclave, reasonable prices, average quality), or Mustafa (24 hr huge mall, wide variety, fixed prices).
Yes, I do know that place well. I can post pictures of my quilt if you are interested to take a look at the fabric.
Hope that helps.