As far as info from the Second Age goes, I'd like to know more about Gil-Galad, the Numenorean colonies (tantalizing info in "A & E", huh?), and the history and movements of the Dwarves. While we're making wish lists, I'd like a more detailed history of the Hobbits, a map of all of Middle-Earth post-Downfall from the hand of the Professor, and a parrot that can sing the Lay of Leithian in Sindarin.
But, as far as the Akallabêth goes, I found
this while poking around on Ardalambion a while ago. I know it's by and large Mr. Fauskanger's work, but it's still fantastic, in my opinion. Definitely some of the best fan-fiction I've ever read, in any genre. Definitely better than the garbage video games that are most of my exposure to Tolkien fanfics.