Peekskill is on the East Side of the Hudson. You will need to get a taxi from there.
You are flying in on Sunday night - correct?
You should be okay, barring any unforseen major delays. Like I said, take that emergency number with you and call them if you or anyone on the gov't paid flights get delayed. They will help you. They will come and get you.
A couple of years ago a bunch of incoming New Cadets were stuck at various airports in the Midwest because of serious t-storms. Some were late - very late on R-Day. They arrived in the afternoon. But they got there in time for the parade and Oath ceremony. They didn't have any repercussions because they were flying on the gov't's dime. Would be different if they went privately.
Just don't worry too much.
I can always drive into Newark on Sunday night and pick you up.