Rates I face happily at places to eat (10)

I believe the answer is:

cafeterias

I'm a little stuck... Click here to teach me more about this clue!

'places to eat' is the definition.
I can't judge whether this definition defines the answer.

'rates i face happily' is the wordplay.
'rates i face' anagrams to 'CAFETERIAS'.
However, I am not sure how this is indicated.

'at' acts as a link.

Can you help me to learn more?

(Another definition for cafeterias that I've seen is " Eateries".)

I've seen this clue in the Sydney Morning Herald.

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