“Do you want to go for a stroll along the river?”
You're taking a girl on a date. You're trying to suggest fun things to do together. There's a pretty river near you, so you suggest this.
Do you want to go for a stroll along the river?
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This is one way to suggest an activity. Use this when you're being polite and not sure if the other person will agree.
If you're more confident, you can say:
Why don't we go for a stroll along the river?
To "go for a stroll" means to walk somewhere in a slow, relaxed way for enjoyment. People usually "go for a stroll" in a park, around their neighborhood, on the beach, etc. Use it like this:
It was a really pretty afternoon, so we went for a stroll and then sat at an outdoor café for an hour or two.
Use the preposition "along" to describe walking next to a river. "Along" is also the word to use to talk about things that are next to a river in several locations:
There are some pretty yellow flowers growing along the river.
You can also use "down" or "up" to talk about walking next to a river. "Down" is the direction that the river is flowing in, and "up" is the direction that the water is coming from.
I walked up the river for about a mile, then turned around and walked back down.