Obscure place to shop, having note for daughter (6)
I believe the answer is:
arcane
'obscure' is the definition.
(I've seen this before)
I don't understand how the rest of the clue works.
(Other definitions for arcane that I've seen before include "Ace ran, being mysterious" , "deep" , "Requiring secret or mysterious knowledge" , "Mysterious - an acre (anag)" , "cryptic" .)