Nymph with broken heart goes to America (8)
I believe the answer is:
arethusa
'nymph' is the definition.
(I've seen this before)
'broken heart goes to america' is the wordplay.
'broken' indicates an anagram.
'goes to' means one lot of letters go next to another.
'america' becomes 'usa' (United States of America).
'heart' anagrammed gives 'areth'.
'areth'+'usa'='ARETHUSA'
'with' acts as a link.
(Other definitions for arethusa that I've seen before include "wood nymph" , "Orchid" .)