Harajuku station is right by the entrance to the shrine and it's about 300-400 meters walk. Zoom in on Google maps.

There is parking inside, which brings you about 100 meters from the shrine. But you see cabs and limos (for wedding parties) go closer and the linked map shows that these cars enter from the northern entrance rather than Harajuku. http://www.meijijingu.or.jp/english/map/1.html Note the green markings (for car traffic) with a loop right near the shrine. So if you want door-to-door service then explain this to the driver and take the northern entrance.

I find shrines and temples to be quite boring. The main thing of interest with this one is that you usually see a wedding party. It was built ca. 1920.