I have caught the bus from Yorkeys to Palm Cove for a few hours.
Change at James Cook University station.
Having said that, Airlie is the place to go ashore for a beer.
'The Pub' (Airlie Beach Hotel) is a good local spot.
First pub you'll come across after walking into town from the tender.
Whilst eating tables are in front, behind those there is a separate counter top with bar stools which overlooks the Esplanade.
Advise for next time, if possible try to book a smaller ship which is able to dock at Cairns.