From maps all i can tell is that only North, south and west Modor is protected by mountains. Anywhere East of Barad-dur and Gorgoroth and mt doom is left relatively exposed and unguarded.
Would it have been easier, though longer for the fellowship to go east and enter modor from the East? Though you have the men of Rhun and little doubt it is a perilous journey, it would not be as dangerous as the path the hobbits undertook, through the most heavily guarded side of Mordor.
1 it was indeed very dangerous 2 they needed to go there as fast as possible, there was no more time there might also be other quotes ,I however only know this one: "Neither he nor Frodo knew anything of the great slave-worked fields away south in this wide realm, beyond the fumes of the Mountain by the dark sad waters of Lake Núrnen; nor of the great roads that ran away east and south to tributary lands, from which the soldiers of the Tower brought long waggon-trains of goods and booty and fresh slaves." (Lotr, Rotk, book VI, chapter II) there are, I am sure also many other quotes as to what was going on in the east, but mainly the idea is it was inhabited by very many tribes of men, all doing Sauron's bidding. Also entering the plain of Gorgoroth was dangerous from any side. It would rather be easier to take the Eagles and fly if they wanted another plan. Also there would be no more help in the East and no return, a lot longer and a lot more dangerous.
