Lonely in L.A.

Hello all! I am a new East Coast transplant and have been working as a full time nanny for an amazing family since the week I arrived. They live in the Santa Monica vicinity and have an absolutely adorable 8 month old girl. So far, the job has been nearly perfect. I am bonding with the baby and totally adore her and her parents are treating me really well. I feel like a part of the family already. My only problem is this: back in my home town I never had a problem finding other nannies and even mommies to do play-dates with. I had a tight knit group of girls and we were very close, as were the children. We would throw parties for the kid, go to lunch with them, museums, swimming, you name it. It was wonderful socialization for everyone and the days just flew by. My issue is that now that I'm in a brand new place all the way across the country, I am finding it kind of difficult to meet other full time nannies who are receptive to play-dates. I am finding it harder to approach people here for whatever reason; it seems that nannies/moms are kind of clicky in some of the areas we visit and striking up conversation is nearly impossible. I would love to have play-dates and start up a nanny group here. If anyone else is in the West LA area and would like to get together with a sweet baby girl and her nanny, please let me know! Thanks!