I’d do everything in my power to keep that a secret. Should anyone find out about it my neverending time on Earth could be very unpleasant. To prevent that I would wander from place to place, eventually visiting every country on the globe. Yes there are several countries that are extremely dangerous and in some cases not possible to visit, but a country that is a living hell today may be just find tomorrow and the reverse is also true. Look at Croatia, twelve or so years ago it was a warzone but now it is enjoying rising popularity as a vacation spot. Then there is the Democratic Republic of the Congo, which once had five star hotels and was the “Breadbasket of Africa” (granted it was not a pleasant place for the natives) but is now a politacally shattered country with a decayed infrastructure. By living forever I could see conditions in the world evolve over the years, I would even see empires rise and fall.
What would I do as I wander the globe? Most likely I would help people in need. This would range from random acts of kindness to more substantial things that would change peoples’ lives. I would do all of these things anonymously, lest people become to familiar with me. On the other, it might be cool to become some kind of urban myth of an immortal do gooder.