Average cost for a new bathroom is about $5-7k, and a kitchen can cost you anywhere from $5-20k - depending on what you are looking to do (high end or just basic). Keep in mind that having a kitchen and bathroom in the basement may be contrary to the approved usage of the basement, as prescribed by the NYC Department of Buildings. You may want to consult an architect on that.
You should follow the advice in the answers listed by the other agents below. You should also get at least three estimates from licensed contractors. I have one contractor that I used all the time that is reputable. The company's name is The Bathroom King. They do bathroom, kitchens etc.... The person you want to speak to is, Ronnie. You can reach him at 917-293-1985