I don't think you'll find anywhere that isn't "gay friendly", so the real issue is just food and accommodation.
Beauty Point doesn't have much in the way of food options. Carbone's Cafe is great, but closes for a few months in winter. Tamar Valley Motel is totally 1960s and has one of the best restaurants in the Tamar valley. It's a bit unprepossessing from the outside, but nice people and excellent food.
St Helens has some good food. Try the Blue Shed for seafood and the cafe opposite the newsagent (forget its name) is superb for breakfast. It is not well endowed with accommodation choices. Bed in the Treetops is good: http://www.bedinthetreetops.com.au/ Otherwise, the two motels, Queechy and Anchor Chain, are good value for money.
Hobart: there are endless choices. What are your preferences?