Well, this character suffers of vampirism, which complicates things. He plans on living and isn't hostile toward the civilized world.
Instead, he'll continue his experiments. As he keeps looking after the College of Winterhold, he'll see students signing in, studying, leaving, some of them assuming the role of specific magic school masters. He'll watch the next Great War with an intend to do what must be done. He'll talk to the new students of the Way of the Voice about the former members. He'll witness the cycle of life, mourn the death of his mortal friends, outlast most of his ennemies, see new faces, tell stories.
And even if slightly depressed of immortality, he finally assumed his role of guardian as even with Alduin defeated, mystery still shrouds Paarthurnax. Hank will spend the rest of his time watching over him, just to make sure the old one keeps his promises.
Well that would be the 'end' text for my character.