Yes: more specifically, the staff canteens at the airport are open to the public, serving authentic and tasty Singaporean fare at rock-bottom prices! Despite the name "canteen", these are mini-hawker centres with a dozen or so independently run stalls each specializing in specific dishes/cuisines.
There are at least three of these. The one you'll never find by accident is next to Terminal 2: head out from Customs, turn left, cross the road, enter the carpark (2A) and take the elevator up to level 3M, which is marked "Staff Canteen". Here's the illustrated journey, photos mine:
There is a similar but newer one in Terminal 1, detailed instructions here. TL;DR: find Row 13 in Departures hall, take lift at end down to B1.
Finally, there's also a Kopitiam food court in the air-conditioned shopping mall below Terminal 3 (level B2), between the MRT station and arrivals. This is slightly more expensive, but it's also air-conditioned.