could we use vizre also?
It would call for Jesus-like qualities. Or a boat.
"onto the water"? That doesn't seem to be what the English sentence is saying.
Nor is the Hungarian sentence. If you walk, you can walk "a vízhez". But, if it is not meant quite literally, -ra/-re is also used sometimes. Folyóra, tóra, Balatonra, stb. It may or may not mean the water body itself.
What is wrong with lemegy - for walk down?
Nothing in principle, but megy is a much more general word than sétál. Usually this course goes for these translations: megy - to go; sétál - to walk.