would an elevated light railway work in Wellington?

The Chicago L along the Wabash Avenue side of the rectangular downtown loop. (Geoff Churchman)

As noted in the book Wellington Transport Memories, the answer is yes, but it would be unpopular.  In Chicago the elevated or "L" loop around the downtown area is now a civic icon, but it is noisy and it blocks the view of the buildings at street level - although the noise could be significantly reduced with new technology.  However, the unpopularity of the Sydney monorail is a lesson. 

As noted before, the dedicated right of way through the Lambton Quay or Featherston Street thoroughfares option would result in plenty of objections too. So the best option really is for an underground system.