Eight advance polling stations will be in operation around greater Dunedin, while further afield, voters can also make sure they have their election say from some of New Zealand's most distant and remote outposts.
A polling booth has been set up at Scott Base in the Antarctic, while HMNZS Canterbury is delivering voting papers across the Pacific Ocean to Department of Conservation workers stationed on the volcanic archipelago outpost of Raoul Island.
There was a slow trickle of voters at the University of Otago-based polling booth yesterday morning.
The advance station has been set up to cater for students, who, like Ms Eastwood may be outside the electorate on election day, or unable to make it to the polls.
Chief electoral officer Robert Peden said more than 250 advance voting places would be available around the country for people to cast their vote.
"If you're unable to get to a polling place on election day because you're on holiday, working, in hospital or for any other reason, voting in advance is the easiest way to have your say," he said.
Other advance stations that opened at sites around greater Dunedin yesterday are located at Moray Pl opposite First Church, Knox Church Hall, the Mosgiel Senior Citizens Hall and the Nations Christian Church in King Edward St, South Dunedin.
Advance polling booths in Portobello, Brighton, Middlemarch and Outram are also opening in the lead-up to election day on November 26.