You can take MRT and stop by at Raffles area or City Hall area. There are some alternatives like bus too.
The National Gallery of Singapore located in 1 St Andrew's Rd, Singapore 178957. It opens everyday from 10am to 9pm. Here, you can go wandering and seeing the exhibitions in DBS Gallery. It's so wonderful. You are also able to shop here. There are some pretty good quality of restaurant here.
You can also made postcards from their collection and send to you by mail.
This place suits those who love to meet art and culture in one place. You can spend hours here because there are so many artworks to see.
I bought the admission ticket from Klook and it cost around SGD15. When i went here, i checked that the price for the admission is around SGD20 (for foreigner), but it's free for Singaporean.