Interesting question. I've lived in Wellesley for about 30 years. I live in Wellesley Hills, but my office is in Wellesley Square. Wellesley Farms could be divided into two separate areas - upper and lower.
The key to the answers in each area is simply density of neighborhood. The upper farms properties are, generally, on the biggest lots of the areas you've mentioned. 'Wellesley Hills', per se, is further divided into several areas. In fact, the term "Wellesley Hills" tends to be used by us Wellesley folks just to define the 02481 post office - not to define any specific neighborhood. I think you'll find just about anywhere, that the greater the neighborhood density, the more you'll see kids playing on the street and the more you'll interact with your neighbors. People who live near the square, love to be able to walk into town - more and more empty nesters in town search for properties within walking distance to the village.
When my children were young, I lived on a street in 'Old Cliff Estates' where the properties were pretty close together. My kids played on the street, my dog snoozed on the sidewalk, and we did various things together as a neighborhood. After we became empty nesters, we literally moved two streets over, but on an acre lot - we now have privacy and don't see our immediate neighbors that often. I hope this is helpful. The Realtors who work for me live all over town. One of them is President of the Wellesley Mothers' Forum, others are members of Wellesley Junior Service League, Wellesley Garden Club, etc. They live or have lived in areas from Wellesley Square to Poets to Country Club to Cliff Estates and Farms to College Heights to Sprague Estates, etc., We're always happy to answer questions and welcome new families to town. Best, Elaine