Park near Times Square as there are more spots and it's centrally located in terms of trains. That's 8th Ave to 6th Ave and streets 40th to 49th, pretty much. Avenues are N/S and Streets are E/W. 5th Ave is the spine which defines what's on the east side and what's on the west.
Yep, then drive in. Fork over the dough to park in a lot, because street parking will be difficult and may actually cause insanity.
You can manage to walk to the Park, Empire State Bldg, and Times Square, but you'll be tired. Take the train to Ground Zero, and you can walk to Battery Park City and see the Statue of Liberty out in the bay. No need to drive, they're pretty near each other.