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!
I have to second the advice about chain restaurants. So many tourists for some reason want to go to Times Square and eat. The best places are not in TS. They are located all over but none of them are chains. Do some internet searches for the cuisine you want and go from there.
you can also stay in rockland county and take the palisades parkway across the george washington bridge right into the city. another option is paramus, teaneck,fort lee mahwah,montvale in new jersey and 20 35 min from the city depending o which of these locations is chosen.
Another tip is that sometimes people like myself get a hotel near the airport for the night before a trip so that getting to their flight and the risk of car trouble and traffic are minimized. The only problem with that is that the hotels around JFK and LGA charge ridiculous rates and are not of the best quality for the most part. EWR has a full service Marriott that I have stayed at right on property that is excellent and the rates are better than at JFK and LGA. Also keep in mind that LGA airport has horrible mass transit options and can only be reached by bus. JFK has the Airtrain and can be reached by Manhattan in like 30 mins.