Introverts are not by definition antisocial though they can be. They just spend energy to be social. A shut-in is likely an introvert. An introvert doesn't have to be a shut-in. I don't know the mass public mistake where folks assume introverts are the same as people who don't like social interaction. So an introvert can easily enjoy socializing in NYC and seeing people. It just uses energy.
That being said, if you're not going to leave your apartment, choosing a place that's super expensive due to all the things you need to leave your apartment for, you're not making a good choice.