Lots of good advice so far, Being in Hamilton Park for 25 years of course I'll recommend it, but I'd like to address the outdoors portion of your ask. It varies. With a car, there's mountains within 1-2 hrs to the N and NW, and nice more suburban parks closer. Even without a car you can take a train to Harriman State Park in NY, in addition to our city parks and Liberty State Park on the Harbor.

My outdoor thing is kayaking, and we live on a peninsula! There's all sorts of interesting places to paddle within a 20 minute drive, from the NY harbor and Statue of Liberty, to winding tidal creeks and reed mazes on the Hackensack River.

Lastly, about the 'is it worth it?'. That's up to what you make of it. There's people here who never go see theater, museums and music, whether in NYC or one of our great local venues and theater companies. Sad but true.