We spent Christmas 2013 in Canberra visiting my family, which we've done several times since they moved there from NZ. Canberra isn't really a big tourist destination, and after visiting half a dozen times I'm not really sure what to visit anymore. The National Museums are very good however and worth repeat trips.
The only really new activity we did this time was a couple of visits to the Canberra Arboretum, which is a giant tree plantation on 250-hectares of land that was completely burnt out in the 2001 and 2003 bushfires. I've seen the site driving past on previous trips while it was being planted, but it only opened in February 2013 and is proving to be a new drawcard for tourists and locals. The very large site includes plantations of 100 different blocks of different trees and 100 gardens, as well as long walking, biking and horse riding tracks.
The Arboretum was actually quite nice to walk around, despite the lack of shade provided by mostly baby trees from the hot Canberra sun. There are also two plantations of older trees spared by the fires, including these Himalayan Cedars and Cork Oaks planted under direction from Walter Burleigh Griffin, the original city planner of Canberra, and namesake of the big lake surrounding the centre of town. The Cork Oaks were particularly interesting as they are still regularly harvested for their bark (which makes cork, duh), giving dark lower and pale upper trunks.
One thing that I do most times I go to Canberra is to visit the Australian War Memorial Museum, which is an impressive monumental building with a very good collection of military hardware and stories from both World Wars, as well as Australia's other engagements. The WWII aircraft are my favourites, including some of my favourite planes like the P40 Warhawk, and a massive Lancaster bomber named 'G for George' with associated sound and light show every hour! We were at the museum for closing time, where they perform the Last Post ceremony every day including a story about one of the 102,000 names inscribed on the roll of honour.