Do you know of any good but budget-friendly places to stay in New York City?

Can you tell me the specific dates you are looking to travel?  Then, I'll let you know what I can find for you.  You are talking about Manhattan? 

  -Steph

I picked random dates so that you could see what the prices look like.  The prices during the weekends are more expensive than during the week.  Also, the more in advance, assuming that it is not a special holiday weekend, it will also be cheaper.  If you let me know dates, I can be of more help.  Also, do you need to be in a specific part of the city?  Expedia is a very good site to look at since you can see pictures and sort the results based on price, area, number of starts, etc.  I hope the helps. 

-Steph 

I would look at www.expedia.com or www.hotels.com and just find a place that looks decent in the area that you are looking to be.  They are great websites. 

i've used cheaphotels.com for the last 5 years to book hotels. the descriptions they have are extremely accurate and the prices are affordable.

The Carlton Arms Hotel is a kick-ass place. Managed by a bunch of bros who are quite nice and clean. The rooms are all painted in Graffiti style and personalised quite a lot. I was there around last November and liked it a lot. Useless to say it's in the heart of Manhattan and it was quite cheap. Around 70 dollars or less per room.

Enjoy! 

Chelsmore Apartments, in the heart of Chelsea, Manhattan, is a residential apartment building offering beautiful, spacious apartments.
Chelsmore is a pre-war, Art Deco, elevator building with 24 hour doorman service and a warm personal touch. Around 90dollars per room.
205 West 15th Street, New York, NY10011

reservation@chelsmore.com

Yes, but it requires that you can adjust to the hostel dormitory-style of living.

Located at 103rd on the West Side of Manhattan, the HI NYC is safe, near both subway and bus stops, and is remarkably cheap. I stayed there last week for $35/night in Manhattan. Sure, you sleep in a 12 bunk room. Sure, you use shared bathroom facilities. But look at the price! The place is clean, has a gift shop and snack bar, recently renovated shared kitchen facility, flat screen TVs in the upper lounge and a projection TV in the lower lounge. I repeat, it was safe and clean and in Manhattan next to Central Park and it was remarkably cheap. I felt safe and comfortable. Oh, and did I mention the wifi?!

As long as you go in with your eyes open then you'll find this a decent place to stay.

Check it out: http://www.hihostels.com/dba/hostel060003.en.htm 

I stayed in the Chelsmore apartments last year and I agree with judsp above - really good value for money