The ability to predict depends on the cause of the tsunami. Earthquakes can't be predicted, so a tsunami caused by an earthquake can't be predicted. A meteor can be tracked for a considerable time in space before sticking earth so a tsunami caused by an meteor strike can be predicted.
There is also the possibility of a tsunami early warning system. There are currently sensors in some parts of the ocean which can detect a tsunami before "landfall" and provide an early warning system. Think of it somewhat like tracking a hurricane which generally takes a lot longer to reach land.
In a webpage it was reported that "in 1933 HVO [Hawaiian Volcano Observatory] used seismograms to predict (accurately) the arrival of a tsunami from a distant earthquake, and people in low-lying areas of Hawaii were for the first time successfully warned in advance." The word predict here is somewhat ambiguous. the scientists didn't know the earthquake would happen, but recognized that the earthquake would likely cause a tsunami.
Looking at the map below. Where tectonic plates connect, or where there are underwater volcanoes are prime locations to generate tsunamis.