Mum's after awfully nice places of entertainment (7)
I believe the answer is:
cinemas
'places of entertainment' is the definition.
(cinemas entertain people)
'mum's after awfully nice' is the wordplay.
'mum's' becomes 'ma's' (ma can mean mother).
'after' means one lot of letters go next to another.
'awfully' is an anagram indicator.
'nice' anagrammed gives 'cine'.
'mas' after 'cine' is 'CINEMAS'.
(Other definitions for cinemas that I've seen before include "Where films are shown" , "Picture-houses" .)