Gandalf, Sam and Galadriel are probably classic in the same way. Of those, I would possibly think the two Gs to be a bit better. After all, they had much more time to be around to be classic. Though personally, I don't think you can call a person "classic". Unless it was Gollum. I would call HIM classic, but hardly anyone else.
For the same reason, Elendil, who is probably classic figure in Númenorean history, does not go, otherwise I like him. And the same goes for Mandos. He is just another of the Valar, not different from Manwë or Ulmo. They are classic in their own way, more than "normal" people, but if that's enough...
The Doom of Mandos is "classic" in several ways. It's most of all, a "classic requisite of a classic tale" for Middle-Earthians (like when you say, Epic of Gilgamesh or Odyssey here), but also it is "classic" in the same way it is similar to e.g. some ancient sagas from our world: all this being bound by fate is a very classic aspect of lots of these Greek and terrible Nordic sagas and all.
The Void... despite Nog's argumentation, I'm not really buying it. Taniquetil could be considered classic, certainly more than all the other places. From all the places, I would choose it.
I would, however, argue for Gorgoroth being classic. At least, I would not be so fast to dismiss it as some people have. It is the land of evil, the place of the classic battle (of the classic Last Alliance, but that's another thing), and the place of the classic ending of the classic tale from Lord of the Rings. So from in-Middle-Earth perspective (let's say Fourth Age perspective - or our, Seventh Age perspective?
), I would say it's valid.
Like I said, the Last Alliance is definitely a classic. Again, it is a classic requisite of a classic tale - like the fall of Troy in our world, let's say.
And the Noldor, who are undisputably classic requisites of a classic tale, and not of just one: they are pretty classic. There isn't probably anything more... "everyday" in all the old sagas than the Noldor.