Adding a second bathroom

No one can answer this based on info supplied. Where is the plumbing and sewer line relative to the proposed bathroom? In a wall it will share with the existing bathroom? In the basement directly beneath the proposed space? Somewhere other than immediately adjacent to proposed space? Is waste line in close proximity? Is the building you live in cool with this? Will the building permit you to break through the exterior wall to create window for ventilation as you say? Which is it--a full or half bath that you want? A sink and toilet is obviously going to always cost a lot less than also adding a bath/shower stall. What level of finish do you seek: basic, average, highend (a basic renovation for an existing 1/2 bath may cost $5,000 whereas a gut highend reno of a full bath can cost $100,000)?

So...you really need to provide more information. Also, where is building. Manhattan will cost more than Sheepshead Bay.