I’d say either milford/orange area or the guilford/madison area. All four towns on the train line.

Milford/orange will have the shops you are looking for.

Guilford/madison have nice schools - but less of the shops. But you can visit the places you are talking about from those towns. The kids would have to pretty much be in to either soccer or tennis as far as sports goes. (Grew up there)

Give old saybrook/old lyme areas a look too. Its on the train. Nice town. You could commute to the shops in either milford or in the crystal mall area. It would be about 40 min from new haven. Actually old lyme is not on the train, but old saybrook is. But they face each other across the ct river.