Although you are able to find somewhat cheap hotels in New York City, it will be extremely difficult to find a cheap hotel with a great view. You will likely have to choose one or the other. Some sites to research lodging in NYC are here: http://nymag.com/urban/guides/nyonthecheap/travel/hotels.htm http://www.nycinsiderguide.com/cheap-hotels-nyc.html#axzz1QmhGpQHK
There is one relatively cheap hotel in the city of Venice, Italy that is by far the best reviewed in the area. That hotel is the Hotel Al Ponce Mocenigo.
New York City is not renowned for the cheapness of its hotels and when you do come across a cheap hotel room you should ask yourself two key questions: 1. Is there a reason this hotel is charging less than comparable hotels in the vicinity? (For example, it could be because the hotel has just opened or reopened after a refurbishment. These would be good reasons. If it is simply because the hotel is dirty and would not be able to charge more, then this hotel should be avoided.) 2. Are there reviews of this hotel I can see before I commit to pay for a room? If there are - over several websites - and they offer good reviews, then you should consider it safe to book a room.
There are many cheap hotels in the New York downtown. Some good ones are: The Chelsea Savoy Hotel, The Colonial House Inn, The Cosmopolitan Hotel-Tribeca and The Gershwin.
You can find cheap apartments in New York City at www.nycdwellers.com. Another good website is newyork.craigslist.org
You can book a cheap hotel service at eBookers.com which allows you to book a flight that is available to New York with your choices of hotels within your budget range.
I have used orbitz.com in the past with pretty good success. We went to NYC a few years ago (my wife and I) and went for pretty cheap including airfare and hotel. Many travel websites specialize in trips to New York City. Check online sites such as expedia or orbitz.
There are many places to find cheap hotels in Manhattan. In Manhattan, there are some low priced available hotels that can offer a rewarding stay and visit. These hotels are places such as Belnord Hotel, Park 79 Hotel, Comfort Inn, and Holiday Inn Express.
There are several good, centrally located hotels in New York City. Some of these include Park Central New York, Hilton Times Square, The Muse Hotel, and The Night Hotel.
stay in a good hotel cheap but good:)
Hotels that offer low budget friendly deals would include the Holiday Inn Express New York City, Candlewood Suites New York City, Algonquin Hotel, Gershwin Hotel, Affinia Dumont and many others. The site Tripadvisor might be recommended to compare these hotels or find more options. AirBnB is also a good option when a person seeks budget accommodations anywhere in the world.
The Hudson Hotel in New York City does have some very poor reviews that complain of subpar service. Most reviews note that the rooms are very small, so that may be a consideration. The Hudson Hotel tends to have an average review of 3 to 3.5 stars.
Check with CUNY (The City University of New York). They might help you with that.