Today's phrase is "A wild-goose chase".
This means wasting time going from place to place to find something that you cannot find.
Example 1
I went to five stores to find a part for my toilet. But, none of the stores had it. It was like a wild-goose chase.
Example 2
A. Where were you all day?
B. My boss sent me on a wild-goose chase to find his favorite cigarettes. I found out that they actually don't sell them here in Hawaii. What a waste of time!
https://idioms.thefreedictionary.com/wild-goose+chase