First time I went I did it very cheap, cheapest flight could find at the time (£600), spent 5 nights in Tokyo, a week in Kagoshima then a final 2 nights in Tokyo before heading home.
Very lucky having a friend working over there to have as a guide and host.
First nights in Tokyo spent 4 of those in a capsule hotel in Akihabara (no longer there) which was dirt cheap, then one night climbing up Fuji.
That was end of May /start of June as Fuji was only just 'opened' for the season or something. We were woefully under prepared and much hilarity ensued. One of the most memorable experiences of my life so far and one that my friend and I will always talk about the rare times we get to see each other.
Kagoshima was spent at my mates place, then for remaining Tokyo nights had a bit of luxury in a nice hotel
Really helped having a friend over there to show me round and do stuff with, he'd been there a couple of years already.
Did a few onsens, the one in Kagoshima had a nice view over to the Sakurajima volcano, went over to Sakurajima and had a cycle round there, helped my friend out in the school he was working at too which was fun.
Went again 6 years after with work, slightly different being all paid for so had a nice hotel just near the Metropolitan building
Love to go again sometime.