Holders Dundalk have been drawn away to Derry City in the pick of the FAI Cup second round ties.
The tie will be played at the Brandywell on the weekend of August 23-25 when Shamrock Rovers will host the side that knocked them out of last year's competition, Drogheda United.
The only other all-Premier Division match sees St. Pat's travel to Belfield to play UCD.
Cork City will be away to First Division opposition again when they travel to Galway United, Sligo Rovers will host Limerick FC and Bohemians' reward for beating Shelbourne is a home tie against either Longford or Athlone Town.
The draw also sees non-league sides Crumlin United and Lucan United face each other while Glengad United will play host to Premier Division side Waterford FC.
All games will take place on the weekend of August 23-25.
Glengad United v Waterford
Sligo Rovers v Limerick
UCD v St. Patrick's Athletic
Shamrock Rovers v Drogheda United
Derry City v Dundalk
Galway United v Cork City
Crumlin United v Lucan United
Bohemians v Longford Town/Athlone Town