Why Did Isildur Cross the River?

[Rumil]

I expect Ibrin has the right of it.

Although perhaps the Gladden Fields were more marshy and thus impassable on the Western side, making it a sensible idea to go along the Eastern bank of the Anduin. As long as no interference from Dol Guldur was expected.

Of course at this stage it was still Amon Lanc, and Sauron had not yet occupied the place.