I've only been in Tas for 4 months but I am told that Maria Island and the Tasman Peninsula are a must. Hobart has some nightlife when the students are about, but be aware it is a small town by comparison to Sydney! Also be aware August is the coldest month; bring woolies and rain gear and be pleasantly surprised if the sun shines. I should say I really like it here; I see wildlife in and around town and can get to really quiet beaches and forests in no time.

Water temps in winter are ok in NSW, not so much in Tas! Currently about 20°C open ocean at Sydney and 12°C around Hobart; refer to AODN OceanCurrent for up-to-date sea surface temps (link).

Sydney has good public transport. You don't really need to move around while you stay there. A general comment would be to do the day trips later to allow yourself to get over the jet lag and that your day trip driving south will be very long.

Some comments on the Tas part:
Day 6 - most of the whisky and brewery tours I am aware of are day tours that visit several sights; you wouldn't have time to do that and walk up Mt Wellington. Also don't forget the cider! In fact walking up Mt Wellington is a bit of an effort, because there is only public transport to Fern Tree, from which it is about 20km round trip to the top and back. Might be better to hire a car and drive up in the morning, then do whisky/beer/cider tasting too.
Day 8 - the ferry to Maria Island requires a full day trip or overnight (one ferry each way, am and pm). I have heard it is well worth doing, but be aware when you get back into Triabunna it will be dusk and there will be wildlife about. I cannot emphasise enough how you need to drive slowly at dawn, dusk and night, poised to make an emergency stop, because the wildlife is everywhere. When the signs say advised 45 km/hr they mean it!

And once you get out of Hobart you'll want to plan ahead for meals, even the tourist towns will be quiet because it is winter, so check restaurant opening times or book self catering.

Enjoy!