The most common and most likely answer to this crossword clue is the 7 letter word ASYLUMS
I've seen this crossword clue in The Daily Telegraph
A
S
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More clues leading to the result ASYLUMS
Buddy explains!

The straight part
We know that "places of refuge" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case places of refuge = asylums.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ASYLUMS mean?
ASYLUMS noun- A place of safety.
- The protection, physical and legal, afforded by such a place.
- A place of protection or restraint for one or more classes of the disadvantaged, especially the mentally ill.