Eumarrah in Hobart is a friendly place where you can locate many good organic products such as nuts, fruits, fresh vegetables, flour, pulses and other kitchen basics such as the organic non-roasted muesli.
It is a good place to find the highly-prized Elgaar Farm certified organic products such as their fabulous yoghurt, sour cream and milk.
Over the past year the quality of the fruit and vegetables has improved considerably and much of it is sourced locally, although they now sell conventional (ie products that may have been sprayed) so you need to observe the signs carefully if you want to avoid these.
One of the most constant of the suppliers has been Yorktown Organics which we have featured on this site (here). The following photo shows their greens in the display cooler.

Another has been Tasmanian Natural Garlic and Tomatoes with their 130 different varieties of tomatoes some of which are shown below.

We have noticed a new energy in the shop with the staff being very engaging. It is a welcome sign.
Additional information
Street: 11 Waterton Hall Road
Town/Suburb: Rowella, 7270
Phone number: +61 498 078 198
Opening hours: By appointment only
Their Facebook site contains some useful information: