If you are tight on budget, try:
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Leo House
332 West 23 St, NYC 10011
(212) 929-1010
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This is a clean, safe and tidy (airconditioned) accommodation. I know some people who have stayed there and they were very happy with it.
The prices for rooms here will be difficult to beat, but I would also draw your attention to some caveats:
- they have a 'strange' customer service philosophy. For example, I think advance bookings can only be confirmed over fax no more than X days in advance of the date you wish to stay
- doubly confirm your booking
- not all rooms have their own en suite, but some do - you should double check that too in case you have an aversion to sharing bathrooms
That's what I know from personal experience. Other reviews on TripAdvisor: