See Danny's response, he is spot on, and the Y is within walking distance.
No but the park is very nice. However there is a YMCA that may have the activities you are looking for.
The ymca has great kids programs
There is a small park but no activities are specifically geared towards children. There is a YMCA near the park which may provide the activities you seek. They do bring groups of children to the park. This year the park does have a summer evening program of theater and music.
Not that I know of
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