When it comes to true immortality, you have to think very long-term, so I would say
- Travel the entire world, doing pretty much >>28096
for a long time.
- Once humanity starts to colonise the Solar System, start travelling between planets.
- Get bored of this or maybe all of humanity starts uploading into some sort of Matrioshka brain so take off and go interstellar, checking out some Goldilocks planets for alien life.
- Find the galactic equivalent of the internet and surf it, learning new things from alien cultures. (There are bound to be aliens out there even older than you, right?)
- Spend eons wandering the galaxy. If you're impervious as well as immortal then you could just meditate for centuries at a time while your body flies raw through the vacuum.
- When you get completely bored and want to end it, throw yourself into a supermassive black hole.
Also, the film Only Lovers Left Alive is on-topic and a really good movie.