East Ayrshire - Kilmarnock specifically

Hi everyone. We have been living in Kilmarnock for a good few years now and bought our first house here. Our son will be starting school in the next few years. O know it’s still a few years away but we are due to renew our mortgage again at the end of this year and the plan was that instead of taking out a new deal on this house we would buy something bigger and move to East Ren to get into their school catchment. Unfortunately, that timeline isn’t going to work so it’s either staying where we are with catchment school of either Hillhead or Onthank primary. Are these good schools? Or does anyone know where the good schools in Kilmarnock are and we could look at buying our next house in another part of the town? Thanks x