The first one I saw last time was a hotel - don't remember the name - in Queens Village - at least 4

I am not sure what you are looking for in terms of the area you want to stay in. When I was in the city in March I stayed list of all cities in florida at a place called Hotel Newton, it is between 94th and 95th on broadway. It was a great place that filled all of my needs. It was a clean,very clean, a diner type place next door to get a cheap bite to eat, starbucks across the street, the subway is right there.It is on broadway and my room faced the street so it was a little noisy at night but I was so tired I went right to sleep. The rate I had was $135 with two queen beds.
Look here - but keep in mind, "from" means "FROM" - usually the smallest rooms in the low, low, season. June rates will be more, and bigger and/or en suite rooms are also a little pricier. They are, however, the best values for NYC hotels....
Some are not in or anywhere in Manhattan - at least 45 minutes away - and some are in neighborhoods I cannot recommend that a tourist stay in. (NYC is the safest large city in the country - but there are some areas that are marginal - and some where you should not walk after dark.)
The Youth hostel on 103 and Amsterdam ave is a place where many young people stay and it is in a decent list of all cities in florida area. I did not stay in the rooms there but I had a Sierra Club meeting there and I did not hear any complaints from people who stayed there
I am a bit suspicious, as there is this post by a first-time poster and another post asking the same thing (need cheap NYC hotel, w/no other info provided) by another first-time poster, Pinnow24. Am going to wait and see if either of these folks come back with more info, etc before taking time to respond.
I thought the first listing - International Student Center - had been clsosed due to it being an illegal hostel. Also know the Marrakech has a terrible reputation (claim to be a hotelbut mostly a hostel and in a state of disrepair).
The first one I saw last time was a hotel - don't remember the name - in Queens Village - at least 45 minutes from Manhattan by bus and then subway - and definitly not a tourist area - or a neighborhood I would consider safe never mind pleasant. (I don;t see the last one now, not sure why.)