I have no knowledge if such a phenomena exists in any other part of the world but here in India we have the privilege of watching sunrise and sunset at the same spot .
Kanyakumari which is located at the lowest tip of India is where the sun rises and sets at the same spot.
I have been there but the day we arrived there were heavy clouds and so lost an opportunity. I do not suppose going there again would be worth its while.
Kanyakumaari is a place where 3 seas meet – Indian Ocean, Bay of Bengal and the Arabian seas
Watch this video
Do you know of any other place where the sun rises and sets at the same time? You can write that in your comments