How would you pass your eternity.
Before answering, consider how long the eternity is. If i were immortal, i know what i would do in the beginnings. Do deadly stuff, travel, a few hundred years in school, etc... But after a few hundred/thunsand years, when you pretty much did what you wanted and still have a few years before you, what would you do?
Like Asimov said in Fondation (don't remember what book exactly) you can do ANYTHING with 2 factors. Time and ressources (like human ressources). Basically, If you have an impossible project, it can be done in a year with X people, or in a million year with 1.
I would start colony on a planet outside the solar system.