All you have to do to keep relaxed about this is to think of your own experience.How many tsunamis can your remember besides the big one in the Andaman Sea?None ,I'll bet.That's because these events are rare.
We will never see another tsunami the size of the one a couple of years ago in our lifetime.So chill out and enjoy the beach.There is nothing to worry about.
The chances are much higher for the North and West, because Indonesia is in the "ring of fire", a belt of volcanic instability. New Zealand is also potentially unstable, but if anything happens there, we will have plenty of warning before a tidal wave crosses the Tasman. The probability is < 1 in 1000, of anything big enough to worry about in your lifetime.
Don't worry this time you will not be affected. But we can not rule out the possibility of attacking your place by Tsunami in future. Be prepared for any disasters. But your west coast of your country may be affected after few years.
I saw a documentary a while back, scientists and geologists have studied the east coast for some time and found evidence to support the fact that a giant tsunami has hit the entire eastern seaboard some time in the past, they are unsure of it's hight but put it close to 8 or 10 meters.
They say there is a fault on the western side of newzealand that is capable of generating such a tsunami.
One disturbing fact of the happening of a large tsunami hitting the east is a little town in southern queensland called Tugun, which i am told is aboriginal for giant wave.
I would not worry too much though, as tsunamis are pretty rare, They are just at the fore front of our minds at the moment due to the 2004 boxing day tsunami.