Interesting and very common question. I just posted an analysis, map and links to example houses for this price range. I focused on NYC commuters viewpoint. You can see at the link below or by going to GreenwichStreets.com.
Basically, Greenwich is a small city composed of a bunch of villages most of which have their own business district, albeit often only a block or two. For the commuter we have 4 train stations and morning and evening express trains to Grand Central. Greenwich also has 11 elementary schools and is a big believer in neighborhood schools.
As to houses we have 66 single family homes in your price range, unfortunately only two these were built this century. We actually have 5 house in this price range built before 1901. The majority of the 66 houses were renovated in the past 15 years. Most of them have a good backyard.
You can reach me at 203-969-7900 if you would like find out more.
Here are the links to the town web sites of Greenwich, Darien, and New Canaan which you may also wish to consider as the New Canaan schools have an excellent reputation and about a 50 minute train commute into NYC.
I suggest that you perform some drive-bys through the neighborhoods in these towns to get a better sense on where you will feel comfortable and happy living and also to learn more about the amenities they offer.
Good luck to you!
Prudential Connecticut Realty
Both towns offer strong public schools & commute times with in your criteria.
It's a great time to buy with interest rates at 40 yr lows.
If you would like more info. please let me know and I will send it on to you.
The different area's are Old Greenwich, Riverside, Cos Cob, Byram, Glenville. Then, of course, there is Central Greenwich and Back Greenwich.
Email me at firstname.lastname@example.org and I will tell you all about Greenwich and send some sample listings.