Good hospitals in nyc

So i came from overseas just a month ago and told my husband before that to schedule an appointment with a dr that delivers at tish hospital (which he probably didn’t do). This thursday i went to tish cause they basically told use to just come whenever the date is close which i was already a few days passed it, they checked n said i was in early labor and sent me back home. Anyways long story short I don’t have a dr here so nobody is going to induce me n i’m about to be 41 weeks which atp apparently i can show up to any hospital. What are good hospital in nyc n westchester county? That offer private rooms and allow 2 support persons (my mom & my husband), with decent food, etc… Ik i’m asking for a lot lol but yea i would just like to know your experience. Thank youu