We've lived in Jackson Heights for over a decade. Our son is a toddler.
There is no green space at all in Jackson Heights that is public. There is a great toddler playground in Travers Park, but it gets very crowded especially on the weekends and weekday afternoons. I grew up in the city, so when I say crowded, I mean so crowded that there is no where to even sit down.
The bigger problem for us has been childcare. Having looked extensively within Jackson Heights, we were fortunate enough to find a wonderful daycare, but had to go outside of the neighborhood. Neighborhood nurseries that we have looked at include the Jackson Heights Early Learning Center, the Garden School and Rainbowland.
When we visited the JHELC Annex, we witnessed a teacher who that was supposed to be reading to the 2-year olds. Only instead of reading, a boombox was playing a recording of the book while the teacher flipped the pages. An email to the Director went unanswered for several days because she apparently only has time to reply to non-urgent emails on the weekends. They have a 1:8 ratio of staff to children for the 2-year-olds. This is a very high ratio of children to staff. The Director assured us that they try to keep it a 1:5 staff to child ratio, but as far as I'm concerned trying is not good enough. They located in a small semi-basement.
We also toured the Garden School nursery, having heard wonderful things about their pre-k program. The people who gave us the school tour were very gracious and forthcoming in providing information. Whereas the curriculum seems well-rounded for the higher grades, the nursery itself felt like an afterthought. The head teacher was begruding when answering our questions. They have a 1:7 ratio of staff to children for the 2-year-olds.
When we visited Rainbowland, the toddlers were seated in front of a large TV watching a cartoon. Enough said.
Just when we thought that perhaps we were being too picky, we did find a daycare outside of the neighborhood with everything that we were looking for. Small class sizes (1:5 staff:child), prompt answers from the administration, daily communications (written & verbal) not just a posted schedule, and friendly, loving, professional service. So it does exist. Just not in Jackson Heights that we could find. What we did find was that the daycares in JH that we looked at sounded great on paper, but were disappointing in person.
In terms of neighborhood vibe, II would say that overall, Jackson Heights is a bit older and more conservative / suburban whereas Astoria is a bit younger and hipper. IMHO, JH is more class-conscious and more self-conscious than Astoria.
We will actually be moving later on this year to another neighborhood in the city with green space that is closer to our childcare provider.
Hope this helps.