Canberra is a nice place to see from on-high but you do not have to pay to go to the top of the Telstra Tower to get a great view. Instead, head south of the Lake to Red Hill Lookout in Deakin. The view is just a nice and there is quite a lovely restaurant (The Carousel) just up the hill.
Unique Suggestions: Try to catch the Botanic Garden as well.
Fun Alternatives: As noted, the Red Hill Lookout in the suburb of Deakin off Stonehaven Crescent gives you a very attractive and free alternative