Go and check out CALVARY BY THE SEA. This was such a great school that Dylan and Talia went to and we really enjoyed Miss Kay who is so awesome!!! The website is http://www.montessorischoolhawaii.com/ link.
Other awesome schools that we went to for my other 3 kids who are older were Hawaii Kai Baptist which is now Hawaii Kai Church and Kilohana Preschool in Niu Valley.
Another preschool option is at Gymboree for ages 3-5 years old in Kaimuki.
Co-ops are where you have to go with your child and there are a few that I know of and if anyone else can post that info too. That would be helpful. Holy Nativity, Waldorf, Aina Haina Elementary, Hahaione and I think Koko Head are a few of them. But, you can also go to tiny tots for FREE at Koko Head District Park or Aina Haina and or Kamiloiki. There isn't a toddler time over the summer due to the summer fun programs. It starts back up in the fall.
New School in Hawaii Kai is called HAPPY KEIKI which is located on Hawaii Kai Dr. That is a part time school and lots of moms are happy with this part-time affordable school in Hawaii Kai. This school was started by a mom who was tired of lookiing for an affordable school for just part- time. So, she started one up herself. Kuddos to her!
Some of my friends had put their kids in Kuapa KCAA school that offers full and part time to parents. Also, they have a swimming program because they are located right next to the Oahu Club. Happy searching!!