Go down to Roppongi and don't act like a drunken American, that will help your appeal to some of the local girls. You can walk from there to Tokyo Tower, you'll go right by the Russian embassy!
Go down to Akihabara, Harajuku and maybe even to Nissan HQ in Ginza. Go at night so you can see the place lit up, it's something else.
Getting to an Autobacs may be harder, I don't know of one in downtown Tokyo proper, there's a huge one in Chiba on the way to Narita though, there's also an old school auto sales place off the expressway too on the way to Narita but I don't know the name of it. If you were really hardcore you could try to figure out how to get to Top Secret of RE Amemiya's shops in Chiba. (JUN may be in Chiba too, I can't remember) Check the D1GP schedule or the Nostalgic Heros car show schedule to see if you're there when something is going on. A trip to Kyoto, Nagano, Nagoya or even Osaka on the Shinkansen is possible for a day long event.