I think your problem will be too many options, not whether such a place exists.

My top choice would be Greenwich, particularly Old Greenwich - very family friendly, easy train to the city (driving wouldn't be easy though, from anywhere), progressive, very safe, and beautiful.

For something less expensive, I'd opt for Fairfield or Milford, both of which are great towns and more diverse as well. Ridgefield is also great but not as convenient. Guilford and Madison too.

Farther afield, places like West Harford, Simsbury and Avon are excellent as well.