The typical way the US system works is that you contact an obstetrician and they take over from there. There will be loads of OBs offices, and you can visit several and 'interview' them.
Your choices depend on your insurance coverage. Will you have expat insurance, where you can use any hospital, or will it be an HMO which is restricted to specific hospital groups? You need to know this before seeing OBs.
Basically, the OB will do your pre-natal care, and meet you in the hospital when you are in labour to catch the baby (L&D nurses care for you in first stage). You stay in hospital for 1-2 nights and see your OB again for your six-week check. You should be able to have all your well-women care at your OB office. Some OB offices have a certified nurse-midwife (CNM) on staff who can provide all your routine care, and deliver your baby if there are no complications.
When you have chosen the hospital, there should be a tour available so that you understand the checking in procedures and the choices available to you.
You will need to sort out a paediatrician for your baby. If you don't take your 2 nights in hospital, you take your baby to see the paediatrician ASAP, and definitely at 1 week. The paediatrician will give you a well-baby schedule for you to come in for weighings and vaccinations.
It can be helpful to find a family health clinic where you have all the specialists under one roof, all compatible with your insurance system, but this is not necessary.
You should be able to make preliminary enquiries before you go.