I have just finished 12 months of study at NTU. I stayed in the Holland Village area. It is much closer to town and has some bars and restaurants to eat at. However it is more expensive.
Staying near NTU is great if you plan to spend most of your time there. Food on campus is cheap. If there are lots of other international students in your class then they will be staying just off campus too. Jurong West is popular with NTU students. There is the largest mall in Singapore just a short bus ride from campus too. Stay around there and hang out with the other international students.
Local students will tend to stay at home and then come to NTU by car or public transport.
If you have local friends or a bf/gf here, then it might make more sense to stay closer to them as that is who you will be spending your time with outside of class.
If you are not a morning person, stay near NTU. The taxi fare is $20-25 during the morning peak if you are rushing for an 8:30am class, which is like 10 times the cost of taking the train/bus out there.
Good Luck with it all!