The question:

The two ways that Frodo considers in order to make his way into Mordor are The Black Gate and The Pass of Cirith Ungol.

These seem to be the only ways that anyone considers taking at any point, yet they both seem nigh impassable due to the dangers i.e. the amount of Sauron's forces watching The Black Gate, and the proximity to Minas Morgul & Dol Guldur as well as Shelob's lair at the pass.

So were these the only two ways that people approaching from the West could get into Mordor?

I can believe that geographically these were the only two ways to cross the mountains from the West, but could one simply walk into Mordor anywhere else, such as coming from the East?

If there were more ways into Mordor, what was stopping Frodo from entering through that way? Was it better guarded, were they unknown to the Fellowship, or would the journey to get to these alternative entrances have been too difficult?

The answer: Possibly. By river or by air.