To what extend did Istari know Middle-earth?

[Morthoron]

Mithadan is correct in his synopses. In addition, Unfinished Tales indicates that the Istari travelled a great deal at first, and that Saruman went with the Blue Wizards far to the East (it is conjectured in the U.T. that Allatar and Pallando might have went East and remained there as emissaries of Orome, as he was the furthest travelled of all the Valar).

We can guess that Gandalf, too, travelled quite a bit, given his different names: Mithrandir by the Elves, Gandalf in Westron, Tharkun by the Dwarves, and Icanus to the South (Haradrim meaning "North-spy") -- indicating he had at least passed south of Gondor and into Harad. But Gandalf also gave the proviso, "To the east I go not," and U.T. states, "Beyond Nurnen Gandalf had never gone."

And although the Istari may not have been familiar with the geography of Middle-earth in the 3rd Age, Gandalf, both in spirit and corporeal form, had been to Beleriand in the very early stages of the 1st Age:

...he [Gandalf] loved the Elves, he walked among them unseen, or in the form of one of them, and they did not know whence came the fair visions or the promptings of wisdom that he put into their hearts.

[William Cloud Hicklin]

...he [Gandalf] loved the Elves, he walked among them unseen, or in the form of one of them, and they did not know whence came the fair visions or the promptings of wisdom that he put into their hearts.

Given the context of that quote, I had always assumed the reference was to Valinor, not to the Great Lands

[Morthoron]

Originally Posted by William Cloud Hicklin

Given the context of that quote, I had always assumed the reference was to Valinor, not to the Great Lands

I'm thinking the Elves in Valinor wouldn't necessarily need promptings of wisdom or fair things, would they? Unless, of course, we are talking about just prior to the Kinslaying.

There is precedent of many Maiar (Melian being one who remained) and a Valar (Orome along with his entourage) visiting the Elves in the 1st Age. It's not like they had any prohibitions in that early age of Arda. Olorin in spirit form would not require a ship as a conveyance.

Consider this quote:

"That Olorin, as was possible for one of the Maiar, had already visited Middle-earth and had become acquainted not only with the Sindarin Elves and others deeper in Middle-earth, but also with Men, is likely, but nothing is [> has yet been] said of this" - Peoples of Middle-earth

And then there is a possible meeting of Olorin with Galadriel in the 2nd Age concerning the "Elessar"

"...Olórin (who was known in Middle-earth as Mithrandir) brought it with him out of the West. And on a time Olórin came to Galadriel, who dwelt now under the trees of Greenwood the Great..... And when Olórin had told her many tidings she sighed, and said: ‘I grieve in Middle-earth, for leaves fall and flowers fade; and my heart yearns, remembering trees and grass that do not die. I would have these in my home.’ Then Olórin said: ‘Would you then have the Elessar?’ ....And he held before her the Elessar, and she looked on it and wondered. And Olórin said: ‘This I bring to you from Yavanna. Use it as you may, and for a while you shall make the land of your dwelling the fairest place in Middle-earth....' " -- Unfinished Tales