^Just to add, if you went with J-D, you have a youth theater nearby in East Syracuse and Manlius has a small movie theater that plays classic/independent films.
https://www.sctkids.com/
https://www.manliuscinema.com/
There are plenty of arts based venues/events/museums in the area as well.
https://www.syracusearts.net/
https://www.cnyarts.org/
Now if you want a specialty School, you do have some programs in the Syracuse City SD like the Latin School, the previously mentioned Institute of Technology at Central and the International Baccalaureate program at Corcoran High, among others. As mentioned, within the city, the East Side puts you near Syracuse University, SUNY-ESF, SUNY Upstate Medical and Le Moyne College.
As for other areas, I’d say a town like Brighton outside of Rochester, Amherst outside of Buffalo(particularly the Amherst Central and Williamsville SDs), Colonie in between Albany-Schenectady-Troy, Niskayuna next to Schenectady, Vestal in the Binghamton area, New Hartford next to Utica and Ithaca(which is an Enlarged city SD that covers suburban and rural areas outside of the city). All of these towns have some degree of a college/university influence and are near venues in the main city or nearby towns. All have highly regarded schools too.
There are other places that could also work(Clinton, Hyde Park, etc.), but those are some that come to mind right away.