The published
maps indicate that there might have been a pass over the Ephel Dúath (
Mountains of Shadow) into
Mordor at the head of the Poros River, the border of South
Ithilien and South
Gondor; however, there is no road or any indication of a
fortress there. There is no mention of any of
Sauron’s forces coming from any pass at the head of the Poros in
Return of the King, either, although “
absence of evidence is not evidence of absence.”
There is also an old
map that shows a pass into southern Mordor at the head of the
Harnen River, the border of South Gondor and
Harad, called the Nargil Pass. The existence of the Nargil Pass makes perfect sense: it allowed easy transit between
Umbar,
the old Númenórean fortress-port, and Mordor, and also allowed faster access to Khand, an ally of Mordor south and east of the mountains. I think I recall that there was some indication of a fortress there, but the markings did not make it into the published map.
Some of the oldest maps (published in
History of Middle-earth) indicate that there might have been a difficult pass over the Ered Lithui on the north end of the south-pointing spur on which
Barad-dûr was built, and another halfway between the spur and the eastern end of the Ered Lithui; but as with the other presumed passes, there is no indication of either of these in the published maps.
And of course all of eastern Mordor was open to Rhûn and Khand.
In any event, none of these would have been in the least useful to
Frodo.
───◊───
(added much later…)
To the intent of your question,
Nameless Thing, Frodo really had no other viable options. As it was, he only just got through, or rather
Sam did, and that “mainly by good fortune, as it is called.”
Faramir was too young to know about the peril of
Shelob;
Gandalf knew and was both worried and perplexed;
Denethor (and
Imrahil, too, likely) knew, and after Faramir fell under the
Black Breath, fell himself into suicidal despair.
Had the
Witch-king and garrison of
Minas Morgul maintained their normal vigilance,
the Ring would have been captured in the valley of Imlad Morgul; had the garrison of
Cirith Ungol done its duty, they’d have captured it; had the patrol from Minas Morgul adhered to protocol and not rebelled, they’d have prevented its escape; had Shelob not been foiled, she’d have killed both Frodo and Sam, and the garrison of Cirith Ungol found it.
“[G]ood fortune, as it is called.”