I'm interested in the same information, Katherine. Hope we get some answers. I can tell you we've been looking in Honolulu in the Kaimuki and Diamond Head areas (the area of Waikiki closer to Diamond Head). There are homes with yards here and Kapio'lani park is a huge beautiful green space...which I believe is home to the biggest farmers market on the island. It's also relatively close to a Whole Foods for other food needs. I was meandering through the area yesterday and noticed a large sized community gardening spot. I've been told it's a good family friendly area with decent schools (we're unschoolers but it's still good to be surrounded by involved parents.), it's a more affordable area and retains a good deal of walkability, so you may not require a car.
We're also interested in the area around The Ward Center and Ala Moana center. This is a high rise community but we always see lots of kids at the playgrounds around and it's very walker friendly.
I see a lot of babywearing parents and the Ergo is from here, so I'm fairly confident that this a supportive alternative parenting area but I have yet to really find a community. My in-laws live in Waikiki and love it there.
I'm not sure about going outside of Honolulu. I've heard good things about Miliani and Kailua but we've ruled those out as they are too car dependent and, as far as Kailua, expensive.