Some pieces of detailed information are needed...
from Hanzomon Station to Akihabara, Shibuya, Shinjuku and Mt. Fuji Which of the four would you visit before heading back to Hanzomon Station? Or, would you make a roundtrip to each of the four?
Which area around Mt. Fuji do you have in mind? Lake Kawaguchiko?
Do you plan to simply watch Mt. Fuji or also climb it? If the latter, when will you travel?
Should I need to buy JR pass and PASMO card? 7 days JR pass can save some of transport money In order to make a 7-day nationwide Japan Rail Pass pay off, you need to have one or a few other long-distance JR rides.
(The above three posters are not saying whether a JR pass can result in cost-saving for you.)
An IC transportation card (such as a PASMO Card) is not a rail pass. It does not give you a discount in particular, but it can save your time and trouble on handling cash and paper tickets for each short-distance train or bus ride.
If you are not familiar with an IC transportation card, please check "Basic Use" in the following article.
http://www.japan-guide.com/e/e2359_003.html[Hanzomon Station to Shinjuku Highway Bus Terminal]
I recommend you would check in advance your route to the highway bus terminal when you book your bus and purchase your bus tickets.
Hanzomon (Z-05)
--[Tokyo Metro subway Hanzomon Line]--
Track 4: (Z-06) Kudanshita --transfer (#1)-- Kudanshita (S-05): Track 5
http://www.tokyometro.jp/station/kudanshita/yardmap/images/yardmap.gif--[Toei subway Shinjuku Line: Local (#2)]--
(S-01) Shinjuku: Exit 3 --walking (#3)-- Shinjuku Highway Bus Terminal.
(#1) As you see in the map, the two platforms adjoin, and no gate is between them.
(#2) Express trains on Toei subway Shinjuku Line skip Kudanshita Station.
(#3) You walk along the avenue (on your right) for about 120 meters. Passing by a "NTT docomo" logo on your left, you soon find an entrance to Yodobashi Camera. The ticket office of the highway bus terminal is in the same building. The counter for tickets of buses departing on another day is on the upper floor and open from 9:00 to 20:00.
[Hanzomon Sta. to Akihabara Sta. by subway]
You can take the route shown below.
Exit 3 of subway Akihabara Station is near Showa-dori Gate of Akihabara Station of JR.
If you head to Akihabara Electric Town, itfs a bit away from subway Iwamotocho Station.
http://akiba.or.jp/town/img/akibaAstyle83_map.pdfHanzomon (Z-05)
--[Hanzomon Line (#4)]--
Track 4: (Z-06) Kudanshita (#5) (T-07): Track 1 (#6)
--[Tozai Line]--
Track 3: (T-11) Kayabacho (H-12): Track 2 (#6)
--[Hibiya Line]--
(H-15) Akihabara: Exit 3.
(#4) Taking this train at a car near its head, you can be close to the way for Track 1 in Kudanshita.
(#5) Here you should exit Hanzomon Line and enter Tozai line, each through a gate.
(#6) You had better pay attention to the track number, because here platforms differ by directions.