I’m originally from Southern CA, very near where you are from OP, and I lived in NYC for 5 years.
I LOVED it. It is very different, but none of it is personal.
If you need help/ask for directions you will find that most people will be more than happy to help you out, it’s just not a town for small talk.
Also, different neighborhoods have different vibes. There are some great parks/dog parks in the east village and people are more relaxed and chatty there. Midtown East and the Upper East Side tend to be stuffier as there is a lot of old NY families there and they tend to be more insular.
As far as meeting people, I met most of my friends in NYC through work and then through friends of friends. I belonged to a women’s networking group and we had dinners once a month so I met a lot of people through that as well.
Look for free events to attend. Things like art openings in Chelsea, concerts in Central Park (not sure if they’ve started yet), etc.
People are unlikely to chat much in coffee shops or other shops because those working there are very busy and those shopping there are either in a rush or will assume you are talking to them because you want something.
There are so many people on the streets on NYC begging for money, handing out flyers, trying to get you to go to a comedy show, etc that New Yorkers have been a bit conditioned to have tunnel vision when walking the streets/doing their errands. This is actually how I learned not to smile at people in NYC. The people who are trying to get you to go to a comedy show (or sign a petition, etc) will smile at you, if you smile back they launch into their spiel and will sometimes harass you for a block or two.
Going out to bars can be a good place to meet people as well. Once people are out for a night of drinking they tend to be more open to talking to new people.
Finally, since your SO is working, see if he can organize a dinner outing with some of his coworkers and their partners. That way you can maybe meet a few other people in the area so you don’t feel so isolated while you are there.
For what you are wearing, people really don’t care. You will most likely get cat calls/lewd comments from men from time to time, but just ignore them.
Central park during the day is totally safe and a really nice place to be. There’s also the central park zoo which can be a lot of fun. The zoo and some of the museums will have children’s programs during the day and that could help you meet people as well. Although you may be meeting more nannies than moms.