Summer In The City
As a native, I would recommend a summer in NYC without reservation.
There is a trade off in that this is probably the peak tourist season, but as many "natives" desert the city on the weekends (many for three or four days owing to the "summer fridays" combined with judicious use of vacation or personal days) to take maximum advantage of their "summer rentals", you will find that getting access to theater, restaurants and other popular public venues to be a tad easier on weekends.
Plus, there are many "summer-only" events -- such as Lincoln Center summer events, Shakespeare in the Park, which is free, free concerts and opera in the city parks, and summer concerts at several venues just outside the city.
Moreover, Restaurant Week typically runs at the end of June/beginning of July, where you can dine at some of New York's best restaurants at a special prix fixe of $20.0x, usually corresponding to the current year.
Yes, it does get hot, but unless you're alternative is to summer in Iceland or the southern hemisphere, I don't think it's much worse than most other places. After all, that is why they call it *summer*. And unlike Europe, just about every public place is air-conditioned (except the subway platforms), so all you have to do is duck in and out of shops as you hop around the city to mitigate the heat and humidity to a great degree.
Oh, and if you plan on visiting either the Statue of Liberty or Ellis Island, that boat ride is a lot nicer on a hot summer day than on a blustery November one.