Alright, I'll kick this off.
The majority of goldfields in Tasmania are either in the north/northeast or the west coast.
The largest producing mine was the Tasmania Mine at Beaconsfield, near Launceston (over 1 million ounces historically, I think about the same again in the last 20 years until it closed). The largest alluvial field was Lisle, 200,000 ounces of alluvial, no mines to speak of. The origin of the gold at Lisle is still debated.
In the northeast the major fields were Mangana, Mathinna, Dan Rivulet, Alberton, Warrentinna, Forester, Lyndhurst/Waterhouse, Gladstone, Lefroy, Back Creek, The Den, The Glen, and minor finds around Mt Arthur. The west coast had a lot of small workings, but the main areas were Corinna/Long Plains, Mt Read/Ring River area, Queenstown area, Jane River area, and Mt Darwin area.
There was a minor rush in Cygnet/Channel area around 1900, and minor gold has been produced from Adamsfield, the Styx and Weld valleys, the Esperance, Lune, D'Entrecasteaux and Catamaran Rivers.
There is some good info in the Mineral Resources Tasmania library, which is online-searchable. I like to use Google to search it, using the search string: site:mrt.tas.gov.au <search terms here> (without the chevrons). The main resources to get started would be:
Gold in Tasmania by Ralph Bottrill:
http://www.mrt.tas.gov.au/mrtdoc/dominfo/download/GSB70_24_46/GSB70_24_46.pdf
Alluvial Gold also by Ralph Bottrill:
http://www.mrt.tas.gov.au/mrtdoc/dominfo/download/GSMR11_2/GSMR11_2.pdf
You can also put MRTmap (
http://www.mrt.tas.gov.au/mrt_maps/app/list/map) to good use. The mapping engine allows you to overlay mineral occurrences, as well as tenements, and links back to tenement details, so you can arrange your permissions more easily.