Opps, I was going to follow this up after the K-ON pilgrimage post, but I kinda forgot about it.
Before I go on, I must state that this pilgrimage won't be quite as interesting as the K-ON one, because first of all, Lucky Star's a 2004 series, and that means that the hype is mostly gone and there probably won't be quite as many otaku-related stuff to see. Secondly, I'm no LS fan, so I might miss out on a lot of details only a real fan can see. Lastly, Washinomiya Shrine is still a fully functional shrine, so you can't expect them to set aside a whole area for the fans. In fact, the only thing in the shrine that is related to otaku culture are the ema tablets (wooden wish tablets). See Zyl's blog for more.
Anyway, if you're planning to make the trip as well, you can take the Tohoku main line in Ueno, Tokyo to Kuki, then transfer to the Tobu Isesaki Line. Washinomiya is just one stop away... remember that there's a Higashi (east)-Washinomiya station, which is also one stop away on the other transfer line... which is not what you're looking for.
