I suppose much depends on your specialty and experience, preferences in country and financial budget for the trip. For many of the overseas trips, you will be paying your own airfare/transfers as well as expenses toward your room and board at the site. This can be anywhere from $400 to $2000 from my experience, (excluding airfare). Needless to say, your accommodations and provided supplies might be much more rustic (and outdated) than you're used to working and living in the NYC area. My suggestion - start with a shorter trip to feel out the organization and how well the trips are put together before committing to a longer tenure.
I can't recommend Remote Area Medical (Remote Area Medical
) enough. I've been on a number of their trips and return every year for more. I prefer to participate in their U.S. based events (usually 2-3 days of triage and assisting in other areas - medical exams, dental, sorting eyeglasses), but they do a fair share of events overseas as well. Check out their schedule and contact them directly with any questions - they are super nice and appreciate their volunteers.
I've heard good things about Mercy Ships, but I didn't spend enough time in the OR to be of much good to them as a RN. I imagine if you have periop experience, there are many, many good organizations to choose from; so many trips are surgical excursions to established small clinics and hospitals. Good luck and thank you for wanting to volunteer!