Please find my answers to your questions below. Mount Fuji is nearer to Tokyo than Osaka. Your reply will be very appreciated.

Shibuya has a similar local bustling atmosphere as Shinjuku but with a younger crowd. Shibuya is a great place to stay if you like nightlife and shopping in a youthful environment.

Stephen will always and fondly be Hotel Sunroute Shinjuku is a great hotel choice!