Please elaborate on the kind of immortal here. Unkillable? Unaging? Or do you still age and just keep getting older and older? Do you still feel pain? If you lose a limb does it regenerate? If you were atomised, would you just be a scattered conciousness, becoming the screaming in the wind? If we're talking regenerate from anything, unaging kind of immortal, how do you die? When you are done with existence, and have nothing more to do, what then? When everyone and everything is dead, are you left alone, on a dying rock, as the sun expands and you boil alive in pain for millions and millions of years? Would you eventually witness the heat death of the universe and witness the last black hole dissipate through hawking radiation? And that's not even touching on memories! Do you remember everything, or do you get to the point where you forget the names of all your family and friends, your pets, your accomplishments and lessons learned through trial and error? Do you eventually forget your own name? Do you really continue being you?
Anyway, the first thing I'd do if I were immortal is eat some ice cream. I have so much time now, so why not?