As Chris said, a week is not enough to see everything, I suggest to choose one side now and go back for the other side later.
Were it me, I would head west from Devonport, then see Cradle Mtn, Mole Creek, The Nut at Stanley, the northern coast on the way. then down the west coast to Strahan etc and back up the middle via Arthur's Lake, Great Lake, Miena.
Save the north-east and east coast for the next time.
Enjoy!!!
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