Around how much would butt augmentation cost when done in a hospital in NYC?

It sounds like your surgery done in a resident clinic, meaning that your procedure is performed by a plastic surgery in-training, for a reduced fee. This may be an option if you are looking for reduced fees, however, keep in mind that while a board certified plastic surgeon will be "supervising", the surgery and all aftercare is done by the plastic surgery resident. 

Surgical prices vary by region, surgeon reputation, and surgical experience.  Keep in mind however that very few plastic surgeon truly specialize in buttock implants and the first time around has the absolute best chance for aesthetic success. Revision  for botch-jobs are not only very expensive but extremely challenging to achieve at least a good, not great, final outcome. For this reason, I literally have at least 60% of my patients fly in from other states or other countries as far as the Canada, UK, Holland, Australia, Hong Kong, Italy, Germany, India, Saudi Arabia, Turkey, etc. 

Hello dear!!
Thanks for the question and provided information as well.
The average cost varies a lot depending on the city, the clinic and the plastic surgeon. l recommend you to make an appointment with a board certified plastic surgeon to talk about your goals and anything you need to know.
Good luck :)

Options for buttock enhancement include Sculptra, Fat and implants.  I have listed these in order of safest to most risky.  Patients with small amounts of fat may have fat injected followed by injection of Sculptra.  With two to three sessions lasting less than one hour Sculptra injections may produce results lasting two to three years. Often hospital operating fees offset the savings obtained from having a resident perform the procedure without a surgical fee.  Due diligence in researching which procedure is best suited for you and pricing will be quite rewarding.Please consult in person with an experienced Board Certified Plastic Surgeon prior to making treatment decisions.

If you do not have a lot of fat then you are possibly better off getting buttock implants.  If you are talking about having a resident do it, then the fee will be different. You will have to do that research.  Good luck.  

There are generally 3 procedures available for buttock enhancement:
1) Fat grafting, otherwise known as BBL ($6,000 - $8,000): Fat is harvested from ALL areas of the body and transferred to buttocks to increase overall size and to provide contouring.
2) Buttock implants ($8,000 - $10,000): Implant is placed centrally to increase buttock projection
3) Buttock lift: Decrease any buttocks sagging
These procedures can be performed alone or in any combination.Without much fat, it is likely that both an implant and fat grafting will be needed. These procedures done simultaneously will cost around $10,000 - $12,000. 
A consultation with a board certified plastic surgeon would be helpful in providing a more accurate response.