When we tried to get our eldest daughter into a local school a few years ago, we were allocated a school that was several kilometres away. After asking around it seemed that no one thought very much of this school, which was apparently why few local parents had enrolled their children there and why we were "lucky" in being allocated a place.
As foreigners (EP holders), it was always difficult get into a school near your house if it happened to be moderately good (popular) with parents. Forget about the so-called good schools, no chance getting into those as every Singaporean parent has bent over backwards to ensure they get into a higher priority level. Even the moderate/OK schools were filled after Phase 2B (4th out of 7 registration phases). We applied for schools that were mid-way down the pecking order, mostly the CHIJ schools near our house but got no joy.
Since 2012 PRs are now also lumped together with EP holders into the last phase (no longer given the same preferential treatment as Singaporean citizens). The impact is that EP holders have Buckley's chance of getting a half decent school anywhere near their suburb.
Since Foreigners come last and get what is leftover after the first 6 registration phases, another way to see this process is settling for the dregs after everyone else has had their pick of the best, good, moderate/OK, and just below average schools. I am not sure I wanted this for my children, so had no choice but to go the terribly expensive route of International Schools.
Good luck with this, and I hope your experience with getting a place in a local school is better than mine.