I know that noone really know about this, even Valars. Some source guess they go to a new world, where they can build it as they want. Hmm... isnt that make them god? Im not support this idea. What do you think?
Imo, i think they'll come back to Ea, in a new form. Their memories will be wiped out. I think thats the meaning of their "gift", they can forget everything, while the elves have to watch what they loved gone and stacking their grief forever. There need to be some kind of reward and punishment for good and bad people too, so i think Eru will judge them. Good people could be reborn in a good family, or any kind of life they choose. An eagle, or a dolphin for example. Some heroic people could even become an elf maybe? In the other hand, bad people would be born in an unhappy family, or have to take the orc form... Lúthien and Arwen brought me this idea, because the elves said Arwen was like Lúthien had come on earth again. Lúthien chose the mortal life. She die as a mortal, therefore take the same path that every mortal goes. Eru wiped her memories, and send her back to Ea as Arwen.