I'd reccomend the Whyte River walk that flyfisher mentioned - there's a picnic area halfway (at the Whyte river junction), where we saw a monster tiger snake

Just across the Pieman river, there is also a short (duckboard) walk up to a couple of graves.
I remember when we stayed there 18mths ago, we took a day trip (driving) off to explore Trial Harbour, Zeehan and Granville Harbour.
I'll attach a leaflet that the store gave me when asking about walks in the area... but it might be the same thing you already have.