If the hotel is near a PATH station, take the PATH train to 33rd Street, exit the station on Broadwa

If the hotel is near a PATH station, take the PATH train to 33rd Street, exit the station on Broadway (rather than 7th Avenue), and walk to 34th Street, turn right, and walk to the Empire State Building, which is on the corner of 34th and 5th Avenue.
If your hotel isn't near a PATH station, you'll likely have to take a bus into the Port Authority, which will be particularly inconvenient. You'll come out on 8th Avenue around 40th Street. Then you either have to walk or take the subway down to 34th and then walk over to the ESB. There are no subway stations along 5th Avenue, so a bus (going south down 5th Avenue) or walking texas travel maps are your only options.
I agree with J62 that it makes no sense to backtrack to Newark Airport which adds time and a lot of money to the cost of the trip into NYC . But I also disagree with J62's suggestion "1 mile from the Journal Square PATH station - easy walking distance if you are able bodied." Aside from the assumption that a one mile walk to start what's probably a long of touring is something everyone can and should do, it doesn't take into account what that one mile is like. I don't know the area either, but it's certainly not going to be pleasant city sidewalks meant for strolling. You'd have pass under the Pulaski Skyway on that route!
Asuming you have selected it on the basis of price - and if you really don't have hte budget to stay in Manhattan I sruggest youlook at the hotels in Long Island City that are clse tothe subway lines. That area isn't particularly pleasant either, but it is safe - and you are only 10 minute from Manhattan on the subway.
The "directions" provided by this Red Carpet Inn are well into the range of fantasy - it's at least an hour from JFK or LGA. Have you looked at the reviews on tripadvisor? Many are extremely critical - and the only people who found it convenient were the ones traveling by car - access to public transit seems to be very poor, especially at night.
Oh wow ... is this a bad location. Hopefully, you're not here just as a tourist because it's going to be a nightmare texas travel maps to get into the city from there. It's also a relatively desolate area and may be scary at night.
Take a taxi to Journal Square texas travel maps and then the PATH train from there. I don't think I'd try to walk ... it may not be entirely safe, but I'm not sure about that. Plus it's probably over a mile. The hotel might offer a shuttle to Journal Square, or they may be able to guide you once you are on the ground.