Any particularly good spots or times of year?
I used to windsurf at a place called Cremorne, which is about a 20 minute drive from Hobart (on the way to Clifton Beach). There's a shallow bay on the western side, often only one metre deep, and is perfect for windsurfing. On weekends if there's a sea-breeze there's often lots of windsurfers.
Another spot (although less popular) is midway point (just north of the airport) which has two shallow bays with not much swell.
Remember to wear a wetsuit if you go though as Tasmanian water is cold! about 8 years ago
Ralph's bay is also really good for flatwater windsurfing as it is often only knee deep all the way across, so you can go about 500m at the same depth without reaching the other side. Great for racing I think and on a good day there are often a couple of windsurfers about.
The Derwent River itself is a popular place to just cruise around but it's a bit scummy and at it's deepest point it is over 50m so it's not the first recommendation. Launch from Sandy Bay if inclined. about 5 years ago