High camp hut below Mt Eliza (very good track) - great views of Lake Pedder & surrounding peaks & ranges;
you could then also go to the summit of Mt Eliza for ec=ven better views. Watch out for the resident mice in the hut tho.
Junction Creek on the Port Davey track - good camping, a toilet 'pod' & amazing views of the Western Arthur Ranges; only a few hours each way.
As already mentioned, Mt Field is an amazing place for easy overnight 'family' type walks with lots of options, some with huts too if thats your preference.
Adamsons Peak with great, if a little exposed camping on the plateau below the peak, a very good track.
Slightly harder but amazing scenery - Square Tarn below Mt Chapman / Burgess Bluff on the South Picton Range; a good track & beautiful camp site.
The extra couple of hour return walk up to Abrotonella Rise for some of the best views of / in the south-west of the Artur Ranges etc. is more than worth it.
I'd recommend grabbing John Chapmans guide book 'South West Tasmania' for plenty of other suggestions:
http://www.john.chapman.name/pub-sw.htmlHope this helps.
Stu.