There is too much to see and do in NYC. Spend time on-line to research your interests and make a skeleton itinerary. The city will be noisy and crowded. If this is overwhelming, most of the streets that run east/west can serve as a respite from the chaos. Away from Midtown, the side streets tend to be more residential or less travelled. It can be quieter. Some east/west roads are major thoroughfares, though - you'll find them easily. The neighborhoods of lower Manhattan are interesting for their 19th and early 20th century architecture and distinct cultural nuances. It's free to walk and there is always something interesting to see or do everywhere. Use the subway. Most people do. People are friendly (unless they're in a hurry), so you can ask strangers if you need directions. The subway is noisy, dirty, and hot. Factor that into your breaking point.
The new World Trade Center complex is worth a visit, but plan to spend a few hours there due to crowds and lines. The view is best on an absolutely clear day. A trip to Ellis Island or the Statue of Liberty will be very time consuming. It's lines, boats, the visit itself, and another trip back. It isn't free. Times Square at night is worth doing, but it's like a carnival on steroids. Anything considered exiting in NYC will involve crowds and noise. It's a major part of the NY experience.
There are numerous museums to visit, all of which are worthwhile. The major ones are overwhelming in size, so you can easily get intellectually overdosed. If they are not crowded, museums can be peaceful and the interior temperatures are agreeable on a hot day. It's a good place to come down from the chaos and see some of the world's exceptional artwork. If it is convenient, the Lower East Side Museum is worth a visit. It's authentic housing from the 19th century, authentic examples of living conditions in that famous neighborhood throughout the years. They are all guided tours and the guides are very knowledgeable. The tours are educational and interesting.
A free, but time consuming adventure, is Central Park. Each area has its own ambiance and the footpaths go on for ever. Each section is a new adventure, but its a lot of walking. It can be beautiful and peaceful, though.
I'm sure you'll not run out of things to do in NYC. Unfortunately, the area known at the infamous 5-Points no longer exists, but if you research some history of New York, you'll enjoy your visit a bit more. There is so much to see without having to spend a lot of money. Naturally, be aware of theft. All major cities have pick-pockets and some of them are very good at their craft. Watch out for one another and protect your stuff. I think that half of the fun in visiting any new city is to just go exploring. Plan to see what you really want to see, then let your mood and energy guide you wherever your heart desires. You are likely to sleep well.
