The fastest way to Tokyo from Narita is the SkyAcess train. 36 mins from T2 to Nippori. Then you'd need to connect to another train to get to Ginza.

I've done the day trip into Tokyo from Narita twice, on the same trip (had SYD-xNRT-ITM-xNRT-ICN). The first was a 12 hour connection, the second 9 hours. In both cases, I used the Keisei Sky Access to Nippori or Ueno.
The first one, I went to the Shinjuku area for about 6 hours (I had to get my bag checked for the JL domestic flight and find a locker to store my laptop for the day before I left NRT). The second time, I went to Akiba and Ueno Park. Spent about 4 hours there, but headed back to NRT earlier then planned to nap in a lounge due to a migraine.

Depending on if you need to do anything at NRT (eg, check/store any baggage, customs, etc), you'll only realistically have 4.5 hours, including travel time, before you need to be back to board your outbound flight.