Here is a list of things to see and do...
Most of these are free, or will cost only a couple of dollars.
Bus (or taxi if you're feeling rich)
- National Museum
- National Gallery
- National Portrait Gallery
- Parliament House (Both old and new)
- Telstra Tower - great for views over the city, plus the restaurant is revolving, be prepared for a $$$ bill if you have dinner there.
- Mount Ainslie (Like Telstra Tower, good views except for free. The famous shot of Canberra looking down to parliament house along Anzac avenue was taken from the lookout up there)
- AIS
-The War Memorial
- Questicon - Great if you have kids, but even Adults enjoy it.
- The Mint (I haven't heard overly great things about the Mint, plus it's kind of out of the way nestled inside a suburb)
- Hire a bike and ride around the lake, Canberra also has some of the best bike paths in Australia (or so we're told)
Shopping
-If your into shopping, the Canberra centre is the giant mall in the CBD, there are also 3 other malls which can be easily gotten to by taking any of the 300 series busses from the city - Tuggeranong Hyperdome \ Woden Plaza (technically Westfield Woden, but the locals still refer to it as the plaza) \ Belconnen Mall (Westfield Belconnen).
- Kingston and Manuka is "the place to be seen" in Canberra. If your after coffees and \ or boutique shopping, this is the place. Just be prepared to empty your wallet if you actually buy anything.
If you have a car
- Lanyon Homestead
- Namadgi National Park. Orroral Valley is a great place for a picnic.
- Tidbinbilla, both the wildlife reserve (watch out for emu's steeling your lunch) as well as the tracking station.
- Cotter - Another good place for a picnic
Getting around Canberra
Unless your planning on only going somewhere close by taxi's are very expensive (Canberra is very spread out). I'd suggest either hiring a car (Canberra is very car friendly, but I would also suggest hiring a GPS) or taking the bus.
300 \ 900 series connects the 4 "town centres" together). From the CP it is about a 5 minute walk to the bus stop where all 300 \ 900 series bus routes go through.
Parking in Canberra (even in the city) is cheap by most major city standards, with the average cost for daily parking in the City is around $10. Out at most attractions it is free, and quite a few car parks offer the first 2 hours free anyway.
Enjoy...