Edinburgh is not just a popular destination for tourists and travellers, but also has a large, diverse expat population.
If you are interested in catching a live rugby match, try and get tickets to see the All Blacks at Murrayfield stadium. Walkabout, is a chain of bars that are particularly popular with expats from Australia, New Zealand and South Africa, and they are sure to broadcast all the major sports fixtures live.
For more information on things to keep you busy in Edinburgh take a look at our What's on in Edinburgh page and the Lifestyle and Shopping in Edinburgh page.
There's the New Zealand Society Scotland (http://www.nzsocietyscotland.com/) but they don't seem to have much of a forum on the website. It might be worth getting in touch with them and perhaps signing up for event newsletters. If you drop them a mail they might be able to point you in the right direction to meet other NZ expats, find other expat groups or just let you know where the NZ-affiliated pubs are so you can watch matches.