Kristin, I was in your exact position just 6 years ago when my husband and I moved up to Connecticut from the Upper East Side. We also wanted to be close to the train and in a walkable neighborhood to make the transition a bit easier. With your criteria, you have a few options, depending on how long a commute you're willing to make. Greenwich is obviously the closest and the shortest commuting distance (about 30 - 40 minutes to Grand Central), but you'll have more of a challenge finding a selection of homes in your price range because it is the most expensive town in this part of Connecticut. If you want to stay along the main New Haven train line, the other towns you should consider are Darien, Westport and Fairfield. All of them have wonderful downtown village/shopping districts and you can find homes that meet your criteria in walking distance to the train and/or village. If you're willing to go off on to a branch train line, then consider New Canaan. It's also a very expensive town, but it has a thriving downtown/village area with shops and restaurants and the train station is right in the downtown area. As far as commuting times, Darien will be about 50 minutes to GCT and Westport will be just over an hour. Fairfield would be the furthest commute at about 1 hour 15 minutes. Any of these towns would provide you with a great combination of suburban life and urban conveniences such as walking to shops and restaurants. If you were interested in a condo, then I would add either Stamford or Norwalk to the mix, where you're more likely to find condos, not houses, within walking distance of the downtown and train stations.
Feel free to call or email me directly (all information is in my profile, just click on my picture) if you would like any other information. I know what you're going through and it would be my pleasure to help you make a smooth transition from New York to Connecticut.