Rotokauri is a great school. Do you know if you are in zone for there? Aberdeen is also excellent and not too far from there, but not sure if you'd be in zone there... Some kids travel from Nawton area to go to Te Rapa school.
Ballots work on a priority system. Obviously in-zone is automatic then for example it might be siblings of children already at the school, then children of teachers/employees at the school etc. The best thing to do is go and visit the schools you're thinking of and ask them how their ballot system works then ask them about your chances of getting in if you're putting his name down this early. Best of luck with your decision.
P.S I know about some of the schools cause I'm a primary teacher in Hamilton