Honestly imo this always works out way better if you have interests and want to learn how to pursue them in the city. That's when things open up. Otherwise, you just end up spending a bunch of time and money basically shopping and getting nowhere. So, decide what you want to do on a personal level and then go find it (and it will be there because NYC has everything).

On a surface level, NYC has everything most other cities have; museums, shopping, restaurants, shows, concerts, bars, monuments and tourist attractions, parks, etc...but these aren't really sustainable as "fun" things to do in the long run (maybe concerts and shows sure, but not everyone is into that all the time). Nor is shopping or bar hopping a fulfilling and worthwhile "hobby" for very long. So you gotta dig a little deeper if you want longevity and sustainability.