Since you're on a time budget, why don't you just take the Staten Island Ferry instead of going to see Ellis Island and the Statue of Liberty? The ferry cruises past both, and has incredibly commanding views of the city. Best part of all... it's FREE!
Regarding cheap lodging, check out the Chelsea Star hotel:
www.starhotelny.com
It's literally a block away from Madison Square Garden, and it's cheap and very artsy and fun! Being a block from Madison Square Garden = 1 block away from Penn Station too. So if you can get a train ticket into the city, you can just walk to the hotel. Everyone always loves to tell you how expensive NYC is. But if you just do a little homework, you really can have an affordable, BIG time there
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