Assuming you'll want to stay within Fairfield County, which will put you in Connecticut but as close to NYC as possible, and just a quick look for homes with at least 5 bedrooms and priced between $1,000,000 - $1,500,000, the following towns came up for you to consider:
Being that you seem to want a more downtown area - and sidewalks - you may want to initially focus on Stamford and Fairfield.
I hope this helps!
Anywhere along the Connecticut Shoreline would probably fit most of your needs - I service the Lower CT Valley as well as the Shoreline, places like, Old Lyme, East Lyme, Essex, Madison etc would fit your needs. We are within a reasonable driving distance of New York but also have a excellent train service. Please feel free to contact me should you wish me to send you details of what is available on the Market. Anne Astley - 860-304-9058 firstname.lastname@example.org
From what you wrote, it sounds like the southern towns of Fairfield County will be best for you - Stamford, Greenwich, Darien, etc.
However, what price range are you looking in? What size house? Minimum number bedrooms and bathrooms? These will be deciding factors as to which towns will work for you.