Any of the three would fit, as you know. There are very subtle differences in meaning. To my mind:
"the poet got inspiration" - straightforward. He went for the walk, and that's what happened.
"the poet found inspiration" - slightly more poetic. Perhaps without expecting it to happen, the poet was inspired during his walk. He found inspiration on his walk as one might find money, or wildflowers.
"the poet drew inspiration" - more poetic still. You draw something out of something else, like water from a well. This lays more emphasis on the walk as containing the potential inspiration, there to be drawn forth by the poet.
[native speaker & writer but not teacher]