Nu,
Relic has hit most of the important points I think. It is difficult to provide you with a definitive answer because there are not many of us looking for 15 knots. Most (but not all) of the people who use this site tend to wave-sail by preference, so we are looking for 20+, and none of us ride floaty boards so 15 knots is 'off the radar'.
The other problem is, because the weather is frontal, it is directionally variable, and there are some directions that are just not worth sailing.
Our prevailing wind on the north coast is W - NW, and in these conditions we have a choice of spots noted by Houston above, as well as Greens Beach and Bakers Beach for wave sailing, and Lagoon Bay and Kelso for flat water, all about 45 minutes from Launceston.
If I had to guess, I would say that it is typically possible to sail one of the surf spots 2-3 days a week on average on our wave gear. If you are interested in flat water and have floaty gear this might give you 4-5 days a week (guessing).
The other side of this coin is the upper end of the wind range - we sailed on Sunday in 55 knots... 55 litre boards and 3.7m sails, and got blown off the water. As Relic said - a wide choice of equipment should give you plenty of sailing, but don't be surprised if, like the rest of us, you don't get out of bed for less than 25 knots. And when the wind is kicking for long periods, you just need to get some recovery time occasionally too.
I don't think that you will be disappointed. Don't forget too, you
might have some study to do on those 'off' days...