Judy S.
Yelp
Highly highly recommend a stop to Mount Takao, especially if your trip to Tokyo is around one week or more! You can take the Keio Takao Line from Shinjuku to the terminal station (approximately one hour, 390 yen each way). You can also take the JR Chuo Line. When you buy your ticket for the train, you can choose some of the "packages" that includes cable car, round trip, etc.
In terms of the mountain itself, if you want to see all the attractions, it's probably a good idea to choose Trail 1 for either up or down the mountain. There are two main attractions - the Monkey Park (costs approximately 500 yen, but very worth it) and the Yakuoin Temple (free). Both are on Trail 1, the most popular and most paved trail. The hardest climb on Trail 1 would be from the bottom of the Takao-san to the Monkey Park, if you're climbing up. If you take the cable car, you can avoid this part of the trail. The rest of Trail 1 is relatively easy to hike. All along Trail 1, there are food and drink stands.
At the top of the peak, you can see Mt Fuji (on a clear day). Though we picked a clear day to go, the clouds seem to congregate around the peak of Mt Fuji. If we strain, we could see it - especially with sunglasses on, it was clear and magestic. But unfortunately, it didn't photograph well. There is also a soba shop on the peak where you can grab a quick lunch (AkebonoTei).
At the top of the peak, you get your pick of trails again. We went up Trail 1 and down Trail 5 (for the Biwa waterfall). Trail 5 is very much a trail. It is not paved. There are not that many people - we came across two couples and a woman with her dog. The trail includes walking muddy/forest paths and, at one point, jumping on rocks to navigate down a (relatively shallow) creek!
We went up Trail 1 and down Trail 5, but it might be a better idea to do the reverse. Trail 5 could be pretty dangerous for a beginner hiker, especially going down the mountain. The early parts of Trail 1 were also hard to climb up (very steep and paved) and would be easier to climb down. All in all, stopping a lot along the way, Mount Takao with all of its attractions took us a solid day to get through. We made it back to Shinjuku in time for dinner!
If you're less interested in the attractions and more interested in the hiking aspect. At the top of Mount Takao, you can choose to continue on to the other peaks. There is a path that takes you up and down various peaks until you get to Mount Jimba, where you can hike down Mount Jimba and take the bus back to the station.