Sorry - too cold for me:>) Start by using Google to find school districts; often you find them under counties; most have a very good site covering everything from curriculum to lunch menues and parent and Department of Education ratings.
We live in Greenwich, CT which is in Fairfield County and have been here 2 years. I have been to the town of Fairfield once, and it seemed like a solid middle class place with a lively main street. Fairfield County is cold in winter, yes, but it is glorious the rest of the year - real seasons, with hot summers. The location allows you to have one foot in New England and one in (or at least near) NYC, which is great if you have visitors arriving from abroad. We don't have kids, but my wife works in the school district. The area around Greenwich is one of the most affluent in the USA, and many of the state schools are excellent, at least at elementary level. As with everywhere, you will find good and bad areas and will need to research to find good schools - but it should not be too hard. We have travelled all over the USA and found places with more character than CT, but we love it here for the access it gives us to some amazing countryside and coastline - and for the fact that it is in the Northeast, which is one of the more outward looking parts of the country with a global mix of people. Great place to live.
Seconding what Drake said. Fairfield is an affluent town in Connecticut. It's got a nice little town center with shops and restaurants. It's a fairly reasonable commute into NYC at a little over an hour. There is a nice little beach area as it's on the coast.