Wow, Port Douglas is ahead of the game here with free web apps. Leading the pack is the community based Keys to Port Douglas which gives great keys to your visit here: 

NEW. A community based web guide for cruise ship passengers

Two great restaurants have their own mobile websites: 
Zinc (free wifi) and close-by is 
Finz (free wifi)

Cheap Eats community web guide:

There are a lot of links to Tripadvisor in which blends in well with local content.
You can also order takeout and have it delivered by Port Chicken and Take-away on
The Target Country store at Port Village Shopping Centre and the Commonwealth Bank Saltwater Building now have free Wifi during shopping hours. Over at Mossman Woolworths has free Wifi during shopping hours.