D.B.
The Westboro Area Jewish Community Center on Oak Street has a great program - they have always been very open to Jewish and non-Jewish children. About half the staff is Jewish, half not, and there is great energy. I'm pretty sure they have extended day options. They've been around for years - my son went there and he is now 19! They are next to the Westboro Tennis & Swim Club, and I think they have cooperative programs with them. They serve Westboro, Southboro, Northboro, Hudson, Shrewsbury, and other towns.
Another great program in Westboro is Miss Tanya's centers - she started with one program and now has 3 at different locations in town. She is terrific and runs very enriching programs. One is in town at the Unitarian Church, one is on Longmeadow Road just off Route 9, and a third one is on Flanders Road I think. The Methodist and Congregational Churches in Westboro also have long-established programs. I have neighbors who have kids in all of them, but I'm not sure about extended day.
Hope this helps.