Designed by Philip Johnson in the 1940s, the Glass House and Philip Johnson Estate are beautiful architectural sites worth a visit. As a bonus, the Glass House is also across the street from Phoebe's elementary school and down the road from her childhood home! Advance reservation and tickets required.
Grace Farms Foundation and the 80 acre property on which it sits is a relatively new site in New Canaan, but a great place for a walk and fresh air. The River building onsite is a highlight, designed by Kazzuyo Sejima and Ryue Nishizaea to embody the Foundation's mission to create grace and peace in local communities.
For those looking for a quick morning run near the hotel, Mill River Park is a small green oasis in downtown Stamford.
There is lots to do in downtown New Canaan, with excellent restaurants and shopping. On Saturdays, there is a farmer's market next to the library with great produce and locally renowned bagels (but get there early before the line forms).