Its behind the duty free shops area - the long corridor where the toilets are near the middle of the Terminal2

I did the same in August. Arrived late morning, around 11am. Dumped the bag in left luggage for which you pay a daily fee (cannot remember how much but it was less than SGD 10). Do check as it is not 24 hours. Caught the MRT into town (allow 20-25 mins). Did what I had to do at Orchard Road, popped into Tangs for a couple of items, got a quick bite at Takayshimaya and hopped on the MRT backed to Changi.

Retrieved bag from left luggage, when to SKL F lounge, picked up a glass of Dom, a plate of satay before catching SQ2 to SFO.