Yep, main range area as John said (was up there a couple of weeks ago and there was just enough snow left to make it interesting without impeding walking). Also south to the Chimneys/Cascades area, and to the north around blue waterholes/coolemon area. Around cbr itself there is Gudgenby, Bimberi, Orrorral area, some nice easy ones around Tidbinbilla (think most of the tracks are open now) or if looking for something really strenuous then could try the Tinderrys (see T. Thomas's book: 100 best mountain walks in Aust) - although I believe most of the latter is off track.
Other options within an hour or two include the Woila area off Krawaree road via the Big Badja (Deua NP). Haven't been that far myself but I'm told it's speccy, a grossly underrated destination mostly on fire trails but a lot of off track if you really want to get among it. Also, with ref to the Castle area, a nice (and more accessible from cbr) alternative is the corang peak/canowie brook area, which can be a longish day walk to a couple of days from the car park at Wog Wog (less than an hour on dirt road north of Braidwood, either along the Nerriga road then turn off or from the B'wood township proper through Mongarlowe... the latter option is shorter but a little rougher but both are suitable for 2WD). This area takes in views of the castle/mt owen/pidj house area and in fact can be extended to include the castle (3-4 days rtn or 2-3 days finishing at Yadboro... not an option if doing it solo without car shuffle).
Ettrima wilderness north of Nerriga has heaps of options but also off track (like Woila, haven't been there either but the photos look awesome).
The Shoalhaven Gorge area has heaps of good-road-accessible half or 1-2 day walks anywhere between Bungonia canyon to Bundanoon (plenty of nice day walks around there too). Best access is from Badjery's spur or the Long Point track at Tallong, about 20 mins north of Goulburn.
Believe it or not this list isn't exhaustive! There are heaps of top quality walks within a couple of hours of Canberra outside the Budawangs or the Snowies... they're just not as obvious (ie. on the doorstep) as they often are in Tassie. The castle is definately one of them but there are dozens of similarly spectacular alternatives if you're worries about the exposure (although I do intend to get up there soon). A few of these I've done and many are on my "to do" list that I've seen from a distance. Others, such as Tinderry, will probably remain in the "too difficult" pile but who knows.
Besides, the Blue Mountains are only a few hours away and Tassie is a 1 1/2 hr flight
Cheers
FB