Thanks for the suggestions. Mitake-san definitely sounds like it's worth checking out, (and the all-you-can-eat food and drinks sounds great as well!).

We did look into the guided tours to Aokigahara forest, but they are not being offered on the days we will be in the Tokyo area. There is a train that would get us most of the way there, and then we would have to take a bus (which might be difficult to navigate for us, since we can read and speak only a little Japanese). We haven't ruled it out completely yet, though.