3 year old need friends?

So I’ve been a stay at home mom since I had my oldest who is going to be 3 in July. We don’t know anyone in our area, and we don’t go out much. I’m petrified of letting anyone else watch my children, from experiences too early on.

My daughter is dying to have friends other than her 1 year old brother. I don’t blame her. I try to bring her to the local playground and indoor pool daily. But there’s never anyone for her to play with. Basically my question is, where is a good place to bring my child with my supervision that she can play with kids her own age?

There’s always 6-8 year old kids to play with, but they’re too big for her to play with. I’m at a loss. Her behavior has been horrible, because she’s bored with her life. I really need to find something for her to occupy herself with.