Hi! We moved to the Bay Area from North Carolina right before my son was due, didn't know a soul and had no family in the area, so your post resonates with me. We had luck with Swiss cheese for date nights--they vet their sitters and we felt comfortable with all of them. You can also chat with them before you book so you have control of your choices. We also used care.com to find our permanent part time nanny and she was great. Another idea if you're not in a hurry--hang around the toddler parks in Oakland and Berkeley and chat with other moms and nannies. If you mention you are trying to find someone you might make a connection.
I started out looking for part-time help for my folks and found my wonderful caregivers on Care.com. You set the parameters for what you need and look for someone who fits your needs. There are lots of people out there, so be sure you interview them, run the background & DMV checks (provided through the site), get references and find the right fit (can you tell I work in HR?). Good luck!
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We have used and like care.com. It does cost a nominal fee, but you can get a lot of good information about the babysitters on that site. We also get the babysitter to come over several times while we stay at the house and do other things to get a feel for the babysitter. anon