Welcome to Philadelphia! I hope the move goes smoothly for you and your family. Let us know when you're settled and maybe we can meet up.
I just wanted to chime in for my neighborhood, West Mt. Airy. It's in Northwest Philadelphia, and it has lots of trees, which is part of the reason I chose this location. It feels like I am still connected to nature here. I moved to be close to Wissahickon Park, and to be within walking distance of the local co-op, coffee shop, and kids consignment shop.
Most of the tenants in my unit have been here for years now. I took a prenatal yoga class right down the street, and I can ride my bike to Valley Green. I personally did not want to have a big city feel to where I live, but I still wanted to be close to downtown. My son is almost 2, and it's been a great neighborhood for him so far. I think there's a lot of support in the community.
It's also one of the more, if not the most diverse parts of Philadelphia- unlike other neighborhoods that seem really homogeneous.
I'd never let my child step foot into the Philadelphia School District schools. I taught in them and they are a wreck. That being said, younger kids have some great options with day schools and co-operative nursery schools, etc.