Accommodation can be a huge problem when you go on exchange to Singapore, especially as a master student. When I received my approval of application to NUS, they told me I should look for alternative housing because they can not offer housing to masters students. Nevertheless, I would recommend to apply for housing, you might end up getting a place after the second or third application round. I got rejected in the first round, whereupon I emailed all colleges and halls and explained my situation. Luckily, I received an answer that they had a cancellation in College of Alice and Peter Tan (CAPT) and if I want they can reopen the application portal for me. Of course I wanted, because finding accommodation by yourself is very difficult and expensive! Location and standards of university housing are very good and the rules aren't as strict as they seem when you get an offer.
Living in CAPT was a great experience. I lived mainly with Singaporeans and made many local friends there. If you are open to meet locals, this is the best opportunity and I would highly recommend to join as many activities as possible in your college instead of only hanging out with other exchange students. This way I learned a lot about the Singaporean culture and tried some of the best food I ever had, Singaporeans love to take you out for food!! In most colleges you have a meal plan, which I liked, especially getting breakfast in the college saved my mornings. And again, a great opportunity to make Singaporean friends. My tip: don't sit on the table with all other exchangers but just join one of the tables assigned to your "house" (eg for me Dragon) and start talking to them. Everyone is really open and they are also interested to get to know your culture but that won't work if you only hang out with other exchange students.