In New York, drink case of beer that’s gross then go downhill (7)

'in new york drink' is the definition.
'brewski' can be an answer for 'drink' (informal term for a beer). I'm not certain of the 'in new york' bit.

'case of beer that's gross then go downhill' is the wordplay.
'case of' says to hollow out the word (remove centre letters) (outsides of).
'that's gross' becomes 'ew' (expression of disgust).
'then' is a charade indicator (letters next to each other).
'go downhill' becomes 'ski' (go down a hill on skis).
'beer' with its middle taken out is 'br'.
'br'+'ew'+'ski'='BREWSKI'

Can you help me to learn more?