If you are gonna apply the visa in person at British Embassy in NY you should get it in the same day. If you are gonna apply it via mail it will probably take around 3 weeks max i would say. Again go check the info in British embassy website. Here is what i found
http://www.britainusa.com/visas/articles_show.asp?i=65013&L1=41000
Mail applications
British Consulate-General
Please note that under the Immigration Rules, an applicant for an entry clearance must be outside the United Kingdom at the time of the application and therefore we cannot accept applications sent from the UK.
Apply using the online system and Federal Express. We will return your documents to you using Federal Express overnight delivery, normally within 5 working days. We will update you by e-mail at each stage of the process and inform you of the dispatch date and FedEx tracking number.
Mailing your application:
Inside the USA: Federal Express will not deliver to P.O. Box numbers and a regular mailing address is required for the return of your documents.
Outside the USA: P.O. Box numbers are acceptable for Belize, Costa Rica, Guatemala & Nicaragua provided recipient's phone number is included. For The Bahamas, a P.O. Box number is acceptable but recipient must attend the local FedEx station for pick-up. FedEx will not deliver to a P.O. Box in Bermuda and a regular mailing address must be provided.
Find your nearest visa issuing post
Paying for your application:
Inside the USA: Pay online with a Visa or MasterCard credit card. If you apply by mail you can send a certified cheque or money order made payable in US$ to the British Consulate General or,
Outside the USA: If you are applying by mail from the Bahamas, Bermuda, Costa Rica, Guatemala, Panama & Nicaragua and do not have a major credit card you should send an international draft with a US clearing bank made payable in US$ to British Consulate General. Applications containing personal or company cheques will be returned.
