Joe,
A few variables here.
If you want a quick timed 0-60 you will have to hit at least 6660rpm in second gear, this equates to exactly 60mph and a standard GTI will pull a genuine 64mph at the redline (7100rpm) in second gear, the speedo will be showing higher but you'll be too busy to notice.
As Hurdy said, you will avoid the dreaded cross plane gear shift into third gear which will take longer than hanging on to 2nd gear beyond peak power.
If it's a straight out 1/4 mile run then the 0-60 increment becomes secondary and you'll be losing time overall by hanging on to the gears until the high 6000's. The standard GTI produces peak power at 5100rpm (mildly variable engine to engine) and torque remains relatively constant (at around 200lbft) until 5000 rpm. Changing up at around 6000 revs should produce the best results. Hang onto the gears any longer and you will probably be slower (it's always tempting to rev the nuts off your car as the red mist decends).
Another 1/4 mile factor to consider is that because of the low gearing in third you'll have to change into 4th just before the 1/4 mile post (third will pull 91mph at the redline and you should be doing around 92-95mph across the line).
Look to run around 15 second times and you'll be doing well.
I meant to ask, are you in a DSG equipped car or a manual?