I chose my OB well before i was pregnant, and kept with her as I liked her style (low key, non intervention, really great putting at ease etc)
Most Drs will only have admitting privileges for delivery at specific hospitals, so its worth considering that, and lots of people will choose hospitals that aren't really near them as a result (I lived in Brooklyn but delivered at NY Presbyterian Downtown in Manhattan)
My OB practice had 5 Drs who rotated on call - as a result I didn't get 'my' Dr for delivery and had someone else
I'd choose your OB based on approach to stuff like interventions (my OB practice for example were anti forceps) how often they get you in for screening / tests etc, out of hours coverage and hospital admitting. Also worth noting that its the nurses who do he majority of the delivery legwork, the Drs will do the last bit (but will charge you handsomely..)
I'd choose my hospital based on reviews, newness of facilities, critical care, rooms etc (its usually a 3 night stay for a section, around 1-2 for delivery)
You can also go down the Doula / midwife route but that gets trickier as technically they are a supporting service rather than actual delivery, due to insurance. However, I know of some midwifery practices around - may be worth that route for pre conception checks?
One thing worth noting is that the section rate generally seems higher than the UK, so worth factoring that in overall. There definitely seems to be less appetite here for 2 days labour / mother struggling and more checks / scans at admitting so they can see where the baby is etc
A lot depends on your health insurance coverage tho and where you go