To rent a car you will need major credit card and a driver's license. You can get an international driver's license in your home country. Also, you're maybe better off booking your flight into US though NYC and staying there 1 day before or after your trip.
By car it will take you between 5 and 7 if not more hours to drive, there are cheaper routes. 390 to 17 to 81 to 380 to 80 with entrance through g washington bridge. or you can go 90 to 87 and pay $15 (including tapan zee bridge toll) in tolls.
You should stay overnight in nyc, as a a trip there will take a better part of the day, or you can take a bus, which stops in Batavia (no need to go to Rochester and catch 3 times a day amtrak that runs only during the day). Go to
http://greyhound.com/home.asp There are 6 busses that leave throughout the day and you can catch one that leaves at 11:30 at night and gets to NYC around 6 am, which gives you a whole day there and you catch a 9 pm bus back, which leaves you in Batavia around 6 am next morning. The only thing is that its pretty tiresome to travel like that. If you can sleep in a seating position, surrounded by people (who cannot afford to fly or rent a car) for an extended period of time, it should be your best option.
that way you don't have to stay in nyc overnight, although nyc at night IS something to experience as well. you can see downtown and midtown all in lights from brooklyn bridge. a fascinating view. or times square in lights. there is a lot to see/do in nyc and a day will feel like not enough. they have double decker tour buses that should be a good way to see most of the city. but you should plan your activities in nyc in advance. good luck.