The elite law schools don’t really have an adjustment for prestige of undergrad college. So going to a less ranked undergrad college and doing well (> 3.8) will make things easier for you. Also you’ll need a strong LSAT score.
Getting into top US colleges for an international with financial need is going to be difficult. You’ll probably end up getting accepted somewhere. But how much are your parents willing to spend? Is it worth spending $300K USD for a degree from your list? Not sure, this is something that only you can answer. But given the great opportunities at National University of Singapore, you should consider staying home for college.