I would become a god and create my own universe.
Time is relative, and that relativity is based upon life span. If one were to be immortal the standard definition and conception of time would no longer have any merit. Therefore the passing of centuries would not be that big of a deal to the immortal as one might imagine.
Since years are not an issue, it would be entirely possible to amass a substantial amount of wealth with little to no effort. Take a significant amount of money and invest into several high return CDs (the banking kind not the music kind), a few Roth IRAs (tax free after the age 59 or so), and savings account or two. Take the money out in a century, reinvest at a better rate if possible, and repeat.
After a large fortune as been accumulated, I would invest the money (with the assistance of programs like NASA) into engineering the first galaxy-to-galaxy transportation. Since time is relative the centuries it would take to reach these other galaxies would seem much shorter than for the average life form(even when taking into account Einstein?s theory of time and light speed travel). Also, due to immortality, my metabolism rate should be astronomical. Thus negating the need to stock the ship with the necessities to maintain the average mortal. Less food and water, more space for things to occupy time such as literature and music. The ship would also contain several DNA samples as well as dormant bacteria and other simple celled organisms.
After, scanning the universe and finding a planet that most closely represents earth (although devoid of life)I would land. Upon the simple act of my arrival, the very bacteria inside my digestive tract as well as the bacteria I brought with me including the DNA samples, would theoretically jump start the evolutionary processes on the new planet. Being the dominant life form (as well as my DNA), evolutionary traits could possibly dictate a trend to resemble myself. Therefore I could possibly create a world in my image.
Witness the birth of life through the phases of evolution continuing to a new space age, and repeat.
I have no idea if this theory holds up to rigor, but I think it sounds pretty cool.