Go to Magohany Town and head east to Ice Path. Go through it and you'll reach Blackthorn City. While you're at it, get the Waterfall a man dropped in there.
you do ecruteack city
Blackthorne city is not in Pokemon Diamond but in Pokemon Heart Gold/Soul Silver
in ecruteak city
goldenrod city.
it is in the city after pewter
By going to saffron city.
it is in goldrod city
goldenrod city in a house there is a lady
on the far left in the city
its in blackthorn city behind the gym
south of viridian city
it is north of cerulean city