People can vote as many times as they like, but for a maximum of 10 cities each day.
When voting closes on February 28, the 20 cities with the most votes will be granted one of the coveted spaces on the board.
Cities which are not already on the list also have a chance to make the cut, with Hasbro calling for "wildcard" nominations in addition to the pre-selected cities.
A separate round of voting between March 1 and 9 will determine which two of the wildcard cities make it onto the board.
New Zealand has just one entry on the pre-selected list - the South Island adventure capital Queenstown, which is currently at number 17 on the top 20 list.
Paris is heading up the leaderboard at the moment, but London, New York and Rome are not far behind, with less than 1 percentage point separating the favourites.
Canada is currently the only country to have three cities in the top 20, with Montreal, Vancouver and Toronto all making appearances. Spain has two entries on the leaderboard, with Barcelona at no. 7 and Madrid at no. 13.
Although voting for the wildcard entries has not yet begun, the website also carries a list of the most-nominated wildcard cities. Taipei currently leads that list, followed by two more Canadian cities - Quebec and Winnipeg, Volendam in the Netherlands and Montcul in France.
Auckland is currently at number 6 on the wildcard nomination list.
To submit your votes, click here.
CURRENT CITY RANKINGS
1. Paris, France
2. London, United Kingdom
3. New York, United States
4. Rome, Italy
5. Sydney, Australia
6. Montreal, Canada
7. Barcelona, Spain
8. Tokyo, Japan
9. Athens, Greece
10. Dublin, Ireland
11. Hong Kong, China
12. Vancouver, Canada
13. Madrid, Spain
14. Cape Town, South Africa
15. Zurich, Switzerland
16. Amsterdam, Netherlands
17. Queenstown, New Zealand
18. Berlin, Germany
19. Toronto, Canada
20. Cairo, Egypt
