The Asian Civilisation Museum is located just opposite Fullerton Hotel right beside Victoria Concert Hall (which is now undergoing renovation). Not too sure whether parking is currently available there but I parked my car at UOB Plaza which was basically $3.50 per entry. Took a short walk across the bridge and I was inside the museum.
The exhibits are all located at the 2nd floor and it was quite crowded. Not surprising really since it was free admission to all. I have always found ancient antiques/artefacts pretty cool so it is worth the visit if you like to see such stuff too. Of course, took a short stroll down the Singapore River too