There's a marine farm in Freycinet/Coles Bay that we visited while there and had the most magnificent oysters and mussels. We bought several dozen of each and took them back to our cottage. They were also selling a ginger soy vinaigrette to pair with the oysters, which was hand labelled "Tetsuya's". When we asked about it, we were told that the restaurant sources oysters from this farm, and had shared the recipe for the vinaigrette.
Kate's Berry Farm was good, but we were there off season, and so it was only jams and preserves and baked goods on offer.
First question, when are you going?
In general, Tassie food outside the two cities is producer led. Most of the food attractions are places producing and selling cellar door, so you go visit and eat. What to eat depends on the time of year.
Have a look at http://www.discovertasmania.com/activ...
In Launceston, Stillwater is the biggie.
Materials on that site are really good, there is a Farm Gate guide. Should be available at visitors centres as well
I would try and get to Bruny Island from Hobart, there are plenty of great producers on the island (cheese, oysters etc)
Berries should be good, try Kates Berry Farm.
East Coast fish is excellent, in Hobart Mures is the big one but there are floating fish boats in the harbour as well. If you fancy lunch with a view Kabuki by the Sea is a really nice stop near Freycinet.