Add me to the list of people growing up in southern part of Mass. The town I lived in is called Walpole. It is everything you require, but the housing may be tough. You may be able to find a 2-bed condo or a small 2 bed cape house for "around" $250K. My dad is an estate agent, and he tends to suggest the towns of Franklin, Norfolk, and Wrentham to young families looking for a "relative" bargain. It may be that a house at that price is a "fixer-upper".
These three towns are definitely small, but are nice communities, without much crime. I would say that diversity probably isn't too great, but that is probably fairly common in the suburbs of Mass and RI. There is a really good outlet mall in Wrentham. There are train stations in both Norfolk and Franklin, with direct access into Boston. I think it takes about an hour on the train. They are also really close to a few major highways (495 and 95).
I like the Re/Max website for browsing for houses. Good luck.