Seat E, right side
On the Tokaido Shinkansen from Osaka to Tokyo, Mount Fuji is on the right. Book a window E seat. The view window is roughly 40-45 minutes after Nagoya, just past Shin-Fuji station.

Access
Osaka to Mount Fuji is roughly 400 km. The Tokaido Shinkansen passes Fuji on the way to Tokyo and is the only realistic way to do this as a day trip. Sit on the E seat (right side eastbound) for the view.
On the Tokaido Shinkansen from Osaka to Tokyo, Mount Fuji is on the right. Book a window E seat. The view window is roughly 40-45 minutes after Nagoya, just past Shin-Fuji station.
All three pass Fuji. Nozomi is fastest (no Shin-Fuji stop), Hikari is best balance, Kodama stops at Shin-Fuji if you want to get off. JR Pass covers Hikari and Kodama only.
Hikari to Shin-Fuji (about 2h10), local bus to Lake Tanuki or Asagiri for Fuji views, return same day. Tight but doable.
Shinkansen to Mishima or Shin-Yokohama, then Fujikyu bus or limited express to Kawaguchiko. Plan 4-4.5 hours one way. Stay one night.
Shinkansen to Odawara, Hakone Tozan loop with Lake Ashi cruise, return to Osaka same day. The most polished one-day option.
A 7-day JR Pass usually pays for itself with a single Osaka-Tokyo return. Order ahead through getjrpass.com.