I currently live in NY and I am very surprised that when people want to visit Manhattan they stay in Manhattan. Here is some advise ...
Stay in Lower Westchester county ex. New rochelle , Pelham , White Plains etc
This will allow you to be just 20-30 min outside of the city with lower prices and direct access via Train to Grand Central then subways.You Can also rent a car and have a short nice drive into the City which I would not suggest being as parking in the city is horrible.
This will also allow you to see some nice places in Westchester county there are too many to list. Plus you will have access by car or by train to Lower CT.
This will save money and aggravation and if you needed to know anything you can always ask me. I grew up here and have lived here for 30 years.
Avoid Chain restaurants when dining out and go for amazing local places!