"beside a stream" is a perfectly acceptable phrase in written English.
You can use it to refer to a physical location that is next to a body of flowing water. For example, "We went for a picnic beside a stream in the woods."
You're walking beside a stream when you come across a water mill.
We were beside a stream that ran along a lightly forested hill, and Mina was digging like mad.
On Opening Day, in April, we would get up in the pitch dark in order to be standing beside a stream at the break of dawn.
The funeral was conducted simply, but with due propriety, in the Rupert Valley, where Napoleon had sometimes walked, beside a stream in which two willows were reflected.
He and a survivor of the Chelmno Nazi death camp are seen strolling on the camp's site, now a poetic meadow beside a stream.
In the crook of a tree beside a stream where the piglets have washed up, white orchids turn blue as wormseed makes its way out of the rotting flesh and into their roots.
Besides a stream of movies, there's his hit HBO series, Ballers, and one of the shrewdest strategies on social media.
Jane imagined herself curled up with a bag of licorice beside a streaming windowpane, reading about the Chalet School.
As they approached a stream beside a village, he recalled, "I knew that, after the bridge, there were no more villages, just open country.
Joseph sleeps in the near distance, as an ox and an ass drink from a stream beside him.
Some are quite famous, like Millais's depiction of Shakespeare's drowned Ophelia, a pale dark-haired lovely floating in a stream beside a grassy bank whose plants are exhaustively accounted for.
