We lived in Park Slope before relocating to Miami 3 years ago. We were looking for the exact same things as you are. We chose to live in Coral Gables. I also work in South Beach. I have to be at work by 8:30 am and it takes me 20 minutes to get to South Beach from Coral Gables.
Our neighborhood is a great family oriented area with lots of things to walk to - library, great community center (with a gym, kids program and toddler playground), parks, A schools and a nice area of shops called Miracle Mile. It's not as compact as Manhattan, but definitely more walkable than most areas of Miami. With the housing market the way it is, there are lots of rentals available. Compared to Manhattan you will get much more space for your money.
On another note, if you are looking for a Mom's group in the area, I belong to a great one called From Careers to Crayons. it's a nice group of women with kids ranging from infants on up. They meet 2x week at local parks, do special outings, have Mom's Night Out, a book club and various holiday celebrations throughout the year. If you are interested in the group, email me offline and I can give you more info.
Best of luck and welcome to Florida.