Yes this might sound so cliche and touristy but my very best tip for a first timer is to for sure do the Hop -on Hop -off Busses. This is a great way to see the city and all it has to offer. Its great transport from place to place and it allows you to learn more about Manhattan & the sights on your way to your destination. I just buy it anyway and use it sort of like a Taxi. You can use it for 45hours and really get to see all the sights ,it really is worth it.
You also get special pricing for all other sight seeing things like the Empire State building.
Best tip is – go for the Gray Line – Well its the red bus. There is a green bus, a maroon coloured bus and then the Red one which is called the Gray Line. This is for sure the better one out of the three . It has over 30 stops and 4 loops so you really get to explore Manhattan. It has more busses thus you never wait too long at the designated stops for your next bus (this is especially useful in winter) It also includes a ferry tour which allows you views of the Statue of Liberty and the New York Sky line from the Hudson. And it includes a free night tour.
I have never taken the others but they all basically go the same routes. Except that the Gray Line has just so many other great things going to it that it wins hands down.
The ferry boat does not stop at Ellis Island or Liberty Island though so be sure to make different plan if you want to go onto the Islands and if you want to see the statue of Liberty from Up close.
Have a fun Touristy Time!