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Your best bet would be to ride the train to Harriman state park. It's a great place to get familiar with being outside, and it was where I learned to backpack solo:
Cell service is decent throughout the park. Turn off the phone if you're not using it
Most trails are close enough to a road where you can get out if there's an emergency
There's high traffic trails and more secluded ones to pick from. Tailor your own path to however long you want to be outside
Trail system is well maintained and marked so you learn to look for trail markers
NY/NJ trail conference makes some of the best maps which helps navigate the park. Bonus points for using the Avenza versions
Going by train means it's accesible for day hikes or extended trips from NYC. Multiple stations to choose from for trail options.
For someone in your shoes, I think here would be a great place to start. Go for a day trip by train and get the hang of the park. Walk around a bit with a map and when you're confident enough to go for an extended stay. Build your own hike by picking a trail length you're comfortable with. I can recommend some trails if you want advice
