Where to stay in NYC as a solo traveller?

I’m a 21F travelling solo for the first time to New York, specifically in March, and I’m looking for recommendations where to stay. I’ve been mostly focusing on Manhattan, but anywhere where you think is safe and somewhat close to Manhattan I’m open to. I’m also open to both hostels and hotels as long as it doesn’t cost an arm and a leg :p. I don’t have a huge budget.