I have stayed near my family and believe that having family support is worth not having other things. I also know that it will be very difficult for you find some place that's much different from where you live now. The same trends happening in your neighborhood are happening all over.
It's good to live in small communities but, unless you grew up in them, they can feel cold and lacking in support. I moved to the coast to live for a year after I retired. My support came from where I had lived, which was just an 1 1/2 hour drive away. I've read success stories about such moves but I suspect those families were either very lucky or they did a great deal of research before they actually moved.
All large cities will have the same difficulties that you're experiencing now. On top of that you will be starting over with finding where to shop, who to have as doctors, and getting to know your neighbors. Rebuilding support systems takes time and is energy consuming. I suggest that you can find ways to make your current living place work using less time and energy than you'd need if you moved. And you have family support which is invaluable. Go back and read some of the posts about families who need help and don't have family nearby.
Research the schools in your area and move into that district either now or when your child is closer to school age. Here, in Portland, the school boundaries change every few years and so that may not help. But while doing your research you can find a friendly neighborhood with reasonably good schools on and surrounding it.
You can learn about neighborhoods by regularly reading neighborhood newspapers and Googling for information on the Internet. You can learn about schools on the Internet. You can learn ways to prepare your baby for success in school. You have a better chance of having a good experience near to your family then moving away to an unknown city.