Is going for a walk a good first date idea?

Anonymous
So this girl asked me out but left it up to me to pick a time/place/location. To be honest I don't think I am really that into her yet so I don't want to take her to a restaurant or something expensive. She suggested the cinema but to me that just sounds boring because we can't talk.

I have an idea to just take her for a walk in the country along the river which leads down onto the old train track. This would give us lots of opportunity to talk but it could get awkward really easily. She also seems more like a city kind of girl to me. Also I am worried that she would think I was being cheap for taking her on a date that's "free".

So do you think this a good idea? Advice please?
Updates
+1 y
thanks for all the answers!
Is going for a walk a good first date idea?
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