Not just home to the capital city
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ACT Environment, Planning and Sustainable Development Directorate
https://www.environment.act.gov.au/ACT-parks-conservation
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This walk begins at Mountain Ck Car park within Tidbinbilla nature Reserve. The track is a fire trail, Quite steep at first then becoming moderate until 'Camels Back' (signed) beyond this a 500 mtr, unmarked but quite well defined track will lead you to the summit. The veiws of Canberra and surrounds from this last section are spectacular. Well worth the $10 reserve entrance fee (unless you get there between 730 and 9 am.
Gibraltar Peak (1,038m), is a rocky outcrop with extensive views over the ACT, including Canberra and Black Mountain to the east. It's accessible via a walking trail or fire trail, or combine the two to form a loop. Locatted in the Tidbinbilla Nature Reserve, it's only 45min from the Canberra city centre.
A scenic and rewarding trail which includes views over Red Rock Gorge on the Murrumbidgee River. This walk is one part of the longer Murrumbidgee Discovery Track from Casuarina Sands to Point Hut Crossing.
Stroll around Lake Burley Griffin and enjoy the national attractions, cafes and parks you’ll find along the way. Do as the locals do and do the ‘bridge to bridge’ walk (Commonwealth Bridge to Kings Avenue Bridge), then make your way to Commonwealth Park, the home of Floriade in spring, but perfect for visiting at any time of year.
A good little walk to the top of Mount Ainslie in the ACT.
Mount Arawang Summit Walk is part of the Cooleman Ridge Nature Reserve and is a park of the mountains, hills and Ridges surrounding Canberra.
A short hike up to the summit of Mount Taylor will reward you with excellent views of Canberra and beyond. It is a good alternative to Black Mountain and Mt Ainslie that enables you to avoid all the tourists and actually hike up a mountain you couldn't just drive up.
Walk, cycle or drive to Mt Ainslie Lookout with spectacular views over Canberra.
A moderate walk that is very well travelled and a known tourist route. It has excellent views over North Canberra.