Check out http://www.baird.com/baird/en_html/indian_ocean/indianocean.html for the before and after pictures.
Assuming that you're about 6' tall, at sea level, the horizon is about 3.29 miles away. Tsunamis in harbor waters seem to run between 20-60mph. Even assuming the wave is at 20mph, it's upon you in about 9.87 minutes. The average male human sprints at about 15mph. If you start running off the beach the second the wave appears on the horizon (not likely, has to be closer for you to see and parse it), the best case scenario puts you about 2.5 miles by the time the wave makes landfall. However, since most people can't run that fast for that far (IIRC, the "civilian reasonably fit" standard is about 8-9 minutes for a mile), you're probably only going to be about a mile inland or so, and the wave will engulf you within a couple of minutes, even if you keep running.
Unless either:
1) You grab your car keys and jump in your car [and don't get caught in traffic], or2) You use your allocation of nine minutes to run to higher ground [such as the top floor of your hotel].