Skip driving a car or taking a cab. These are nightmares in the city. Time consuming and costly. Rather than take a taxi you might want to use Uber or one of the many companies like that that charge a flat fare. The subway isn’t too difficult when you look at a map. There are free apps that will help you figure out the best trains to take and where to transfer. If you prefer, you can get a free map at the ticket booth in subway stations. Of course, everyone will know that you're a tourist then!
Just make certain that you are going in the right direction! AND the subway is usually the fastest way to get around town. If you’re going to be using it quite a bit, it is worth it to get an unlimited card. Buses are great because you can see where you’re going and they also work on the same subway pass and you can transfer for free between the subway and buses.
Subway and Bus Etiquette - On the bus the seats at the front are reserved for the elderly, handicapped and pregnant woman. On the subway you should give up your seat for people in these categories. Also, be considerate, do not take up more than one seat. In NYC that's called manspread as men are often the ones who take up more than one seat.
There is free wifi in the subway stations and cell phone service as well. Also, the new buses that are all blue have free wifi and you can plug your phone in and charge it while you rest your feet and are transported to your next location!
Then there’s also the East River Ferry by New York Waterway that will take you to Long Island City, Queens as well as Williamsburg and Dumbo in Brooklyn to name a few places. Oh, the Staten Island Ferry is free and a nice ride. Good for photos too. In the near future I will have a section on free things to do in New York City.
Bicycle rentals - There are many options for bike rentals. Make certain you check out a number of them and see what you're getting into. Some of them have limitations and are only meant to be short rides of 30 minutes or less. Also, it is illegal to ride a bicycle on the sidewalk in NYC!