Arwen, as has been said, chose mortality. Since mortals were admitted to the Undying Lands, it is, I suppose, theoretically possible that she could have sailed there following Aragorn's death. Whether she would have been admitted is another matter.
But I doubt that she would even have entertained the idea anyway. Being mortal, she would have died eventually, even in the Undying Lands. So why, having taken leave of her father, mother and grandmother (and quite possibly her brothers too) once already, would she want to go through the bitter grief of parting with them a second time?
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Do you mind? I'm busy doing the fishstick. It's a very delicate state of mind!
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