I live in Midtown New York and I'd like to offer a few suggestions. To use public transportation go to HopStop.com for the best options, and a time estimate. I think the bus is best for visitors because you get to see the varied street scene. The important museums have one free evening - check a guide book because entrance fees could get expensive. Try to eat in places like Chinatown, the lower East Side, etc. It's a lot cheaper than midtown. Also see if you can get Groupon for New York - there may be restaurant deals that appeal to you. Also try Savored.com for discounts. Broadway theatre is very expensive. Try to get tickets at TKTS at Times Square.
For things to see - don't miss Ellis Island, the Apple Store at 59th St. and Fifth Avenue, Eataly, Central Park.
Part of the best part of NYC is just "people watching".
Hope you have a great time.