There's a ton of hair salons to choose from at Tanjong Pagar Plaza. I chose this place for no real good reason.
Haircuts are $8 nett, a cut, wash, blow dry is $16 and definitely worth trying. They wash your hair with this squeeze bottle full of water/shampoo sitting in the same chair you got your haircut. The lady massages your head pretty thoroughly for a good 5 to ten minutes and then you are led to the sink where they rinse everything away.
Very friendly staff and service. Once there was a wait of about an hour before I got a cut. I didn't know there was a wait b/c although there were people sitting around, the lady led me to one of the barber chairs, which led me to think I was getting a haircut right away. After poking away on my phone for a few minutes... I realized I was waiting around like everyone else. Just as I was about to leave they started cutting my hair. If people are willing to wait around for a cut here, they must be good.