Hiking around Tokyo is very fun, so good idea.
For Mount Takao, I recommend to skip the beginning of track number 1: it is a road, very steep and quite boring. Starting with trail number 6 or the Inariyama trail is a better option. Then you can walk around the top, go down on trail 3, go up again on trail 4 (with suspension bridge), go down on trail 1 and explore the shrine complex. Then you can choose whether you walk down on trail 1 or take the cablecar. Here is the map at the entrance: https://theselfishyears.files.wordpress.com/2013/06/mount-takao-01.jpg. The hike is not so hard, I did all tracks on one day and I saw many kids, even people in suits.
Mitakesan I remember less well. There I took the cablecar. There is an alternative little winding road you can walk on but it is quite tough. Rock garden was really beautiful and is not far from where you arrive with the cable car (45-60 minutes I think). There a few other neighbouring tops you can explore (Mount Odake/Ootake was one of them). The views from these tops were not very impressive though. I think I would recommend Takaosan more than Mitakesan.
If you are looking for a harder hike close to Tokyo, I can recommend Tsukubasan with its twin peaks (beautiful views over the valley, but definitely a steep hike) and Nokogiriyama ("sawtooth mountain" in Chiba, with the approximately 30-meter high daibutsu, the hyaku-shaku kannon and the so-called jigoku nozoki or "hell's view").