Id also like to be recommended to musuems. Ive heard MOMA is one of the best. Are there others I should visit?

Two specifics:

Ellis Island is a museum chronicling the history of immigration to the United States - most immigrants from Europe in the early part of the 20th century were processed through Ellis Island. It is not an amusement park at all, but it is a fascinating museum.

Yes, Staten Island is a residential borough with nothing of interest to tourists. There are parts of Brroklyn, the Bronx and Queens that might be of interest to tourists. For example, Flushing in Queens has a plethora of Chinese restaurants which some consider to be the best in the city, and The Bronx has Arthur Ave. (better than Little Italy for Italian food), the Bronx Zoo, the Bronx Botanical Garden. The Cloisters is also up toward the Bronx, although it's still in Manhattan. Brooklyn has a variety of interesting neighborhoods.

I don't know if it's possible to find a $100 per night hotel in NY, except perhaps in January or February (and even then not likely) which are the worst weather months (far below your desired 50°+).

Ive done some light research on hotels, not in NY but in Newark, NJ. Ive decided to stay in Newark and transit via PATH/MTA each day of my visit due to the substantially cheaper lodging rates.

Id like to stay at a hotel that's either within walking distance of Penn Station in Newark, or provides transit to/from Penn Station in Newark back to my hotel, and preferably also to/from Newark Intl Airport.

PATH trains do not operate from Newark or the airport. You would have to take a bus to another train (NJ transit)into Manhattan or a bus to get to PATH ,then MTA transit within NYC. Time and money can add up if you do this over several days.

Many hotels in Newark are in unpleasant areas. I doubt there's anything in safe "walking distance" to transit to NYC. It's common for people to try to save money on the expensive NYC hotel rates, but what you plan to do would not be something most of us would recommend, and there will no doubt many more warnings or arguments to convince you to change your plans

I hope you enjoy NYC. You have some misconceptions about the city, but many first-time visitors do.

First, PATH trains do operate from Newark, but it's a pretty long ride (perhaps over 30 minutes each way), and they do not run all night, nor very frequently at all at night (this mean that it may take you over an hour to get back to your hotel if you're not near the PATH station in Manhattan). It's certainly possible to stay in downtown Newark, but I'm only aware of 2 hotels. There's a Hilton attached to Newark Penn, but it's going to cost considerably more than $100 at most times of the year (and by next year, I think there's virtually no chance you'll find one anywhere). And there's the Robert Treat Hotel, which is probably your only alternative (though it also may be more than $100). But hotels close to the airport are particularly inconvenient, and while they have cheap rates, you have to pay $12 to get into the city from the airport, and most of these hotels have free shuttles that run on relatively limited schedules.

I think you'll find a lot to like in Brooklyn. It's one of the most dynamic areas of NYC and has a great restaurant scene as well as art galleries and alot of interest shops. There are a lot of cool neighborhoods there, and some are every bit as safe as Manhattan, some less so but still worth exploring. Some are difficult to reach by subway, though (another reason to stay closer to the city).

I'd also caution that Newark is one of the more dangerous places around NYC after dark, so just keep that in mind. You'll want to do all your going out and dining in Manhattan and then just keep your head down and go straight back to the hotel. If it were me, I'd choose the cheapest room with a private bath (which is in Queens usually which is on the NYC subway system 1 or 2 stops from midtown, so about 5 to 10 minutes rather than an hour). And the area is desolate but safe. These rooms are often around $99 but more usually around $125. You'll probably save enough in terms of time and money to justify staying there. Country INn and Suites Long Island City is generally one of the cheaper options, and it's 1 block from the subway.

NYC doesn't offer any combination tickets that include transit and entertainment, but you can use a regular metro card on both the PATH and subway trains, which cost $2.25 each. So the same card, but you can't get a free transfer from one system to the other.

I do think it's probably far too early to start planning itineraries. I'd suggest you buy a good guidebook to NYC so you won't be confused about so many basic facts (such as the lack of an amusement park on Ellis Island). And then you start trying to decide what interests you and we can help more.

PLEASE do not stay at Newark airport - you will spend 2 to 3 hours per day getting to and from Manhattan. It doesn;t matter how cheap this is - it's just not New York. Granted your budget is super low for NYC - if you go in April (NOT easter) you may be able to get something decent in Manhattan via Priceline. (You want to walk out the door and be in Manhattan - just a few minutes walk to some of the sights - not have to wait for a hotel shuttle, take it to the airport, then take AirTrain to the train station, then NJ TRansit to Penn Station). Also if you stay at that hotel - you are stranded at the side of a highway - no way to get to restaurants or shops - and the hotel shuttle might not run late enough for you to eat in the city or enjoy an evening sight and then get back to the hotel.)

There are some budget places in Manhattan where you might find a deal - look at the Jane Hotel (which has some tiny singles) and a few of the others - and when considering the price remember that you don;t have to pay to trek in from Jersey every day.

Elllis Island has a brilliant Immigration Museum - anyone who told you it has an amusement park has never been near it. (And Coney Island, while a NY tradition - for a lot of reasons - is nothing like a modern amusement park - it's style is very 1940s - although the hay day was the 1920s.)

As for what to see and do - there is enough to keep you busy for months. So stay as long as you can - based on your budget. If there is something you really want to see in one of the outer boroughs by all means do it - but not just for the sake of it - when there is so much else going on.

The Met is the greatest cultural institution in the western hemisphere - but look at the website before you go or you can be there in for days - I suggest sticking to 3 or at most 4 departments

MoMA is great if you like modern art (1900 or so on)

Natural History is fantastic as is the adjacent Planetarium

And there are dozens more - on any subject from the Intrepid air and space museum (with space shuttle) to the NY Historical Society to the Tenement Museum to the Asia Society to the Museum of Sex.

As for Italian food - little Italy is essentially gone - and there are few restaurants there worth eating at. The most traditional Italian is in the Bronx (Arthur Ave) but there are plenty of great Italian places in Manhattan - at all price points.

For other restaurants - you need to tell us what cuisines you like/dislike and a budget (based on your hotel budget you should probably look at very modest restaurants).

"PATH and MTA, from what I understand they are completely seperate transit systems"

MTA is the system in NYC(buses, subways).

"Where do I buy each pass?"

metrocards are sold in every station. Get a $10 one.

"As far as attractions, Hard Rock Cafe"

I dont think it's around anymore.

"should I venture into Brooklyn to satisfy my cravings"

Yes, go to Brighton Beach, Emmons ave, Coney Island ave, 86st.

"Ive heard the Ellis Island has its own amusement park similiar to Coney Island. "

huh? where did u hear that? was it an April Fool's joke?

Friends often stay in hotels in Long Island City to save some money. Perhaps it's time to get a good guidebook and just go over the basics before you start planning meals, etc.?