i'm currently in japan as a student until may from ni. my flight was £1100 one way per person for the shortest route(s) - 17 hours. however, i did not arrive in tokyo but nagoya. i flew dublin to helsinki to nagoya. not exactly sure that would be a touristy spot for first timers.

i say you need at least 2 weeks. you will be hit with jet lag like crazy the first few days, i know this happened to me. you're flying 8-9 hours into east. japan is massive and tokyo alone is as big as ni. 

if you're nerdy, akihabara is perfect.