Save your progress using the gate crystal and leave the building. Now a new party member will join you as a guest - he calls himself Lamont. You can't visit the whole city now, because most of the streets are blocked by Imperial Soldiers. You may visit shops right now, but you won't find many new things. It's best to go straight to Lhusu Mines.
Along the way you'll meet many City Parijanahs. They'll tell you how to get to the mine in case you lost your way. On the first crossroads you will meet the Cartographer guild member.