The opportunities in New Orleans are wonderful, I volunteered with Habitat for Humanity for about a month, and it was an amazing experience to be building houses for Hurricane Katrina Victims that were getting things back together. We slept at the local YMCA and just paid for gas, which ended up being around $30 per person, so it turned out to be an extremely affordable program. My entire living expenses for the month was probably $200, and that was all leisure expenses, meals were provided by the YMCA.
But as far as volunteering abroad, I hear it can get costly!