I just delivered a beautiful baby girl at Kaiser on Sunset and can not say enough about how amazing the experience was. The facility has 2 midwives whom you can choose to see for your prenatal visits and who can deliver your child.
That is about all that will be covered by your insurance, but they are very flexible and accomodating of your wishes.
Their birthing center is great and has only been full twice.
Everybody who saw me at the hospital asked for my birthing plan and completely respected it. They even let me take home the placenta, which is against their policy.
One of the doulas commented that my birth was the most gentle and serene hospital birth she had attended. The staff came to check on me very occasionally and left me to labor with my husband, doulas and mom.
I HIGHLY recommend a doula. I was very well read about labor and delivery and know my body, so I didn't really need a lot of assistance. However, having somebody there to suggest alternate positions and just let you know that everything is okay is a very valuable thing. Twice I got nervous about whether I could proceed with no meds and she reassured me that I was doing great and finished with the hard work. If you can afford a doula, do yourself and your baby that favor. If you are in the Southern California area, check our Tracy at Bestdoulas.com. Her page is infinitely helpful.
I hope my info was useful to you.