I use Dr. Dobie at the Family Medical Clinic on Roosevelt. She practices through UWMC, which is in the U-district. She is my primary care, as well as my OB. I had a really good experience with her and the hospital for my daughter 2 years ago, and, at 35 weeks with #2 things are going great so far.
One thing i like about UW is that they have a lot of experience and support for any sort of complication, so, depending on what your risk is they may have the support you need there. At the same time, with my first birth, they really supported my wish to have as little intervention as possible.
I don't know if Dr. Dobie is accepting patients. However, i've also worked with Dr. Pauwels (sp?) at the same clinic, and i really liked her as well.