You are going to have more upfront expenses then just renting space. Your biggest cost will be your marketing and explaining to potential customers why they should come to you and why you are better then where they go now.
If you want to know how much you actually will need - or as close as you can get - write a business plan - you can start by finding free sample plans online.
Do know that it usually takes a business 18 plus months to at least break even. Thus, you have to finance that 18 plus months. But, in this poor economy - it could take longer - even twice that time. Add in NY and even more time.
Write a business plan and you can answer your own question.
Lastly, want to know what space will cost (or any of your expense items) - then get out there and talk to landlords and find out.
Business Money Today
Small Business Loans & Start Up Loans