If you're going to have this done by a shop in NYC the two I'd recommend most for the job are Bicycle Habitat on Lafayette street and Ifixbyks
on 37th street. Ifixbyks is a repair only shop on a second floor so his rent is lower than the typical shop, and the owner is the wrench and more likely to give you better value for a job like that. There's also a good small shop, Bike Works, near the Williamsburg bridge. It may not look special, but the owner and mechanic is skilled and caring, and most likely to take on a job like this at an affordable price.

For the future, the time to do this kind of work is in the winter (if we have one) when shops are slow and begging for work.