It depends. For a honeymoon, you'll want to stay in some good accomodation, so you'll need more! You won't want to stay in scummy places.
For a decent hotel, you'll need at least $1000-1500 for a week stay in Tokyo.
I'm planning to go for about 3 weeks and stay in hostels, so I'm thinking $5000 will cover it. I was in Europe for 3 months this year and spent about $4000 a month there (including food, hotels and hostels, admission prices etc.), so for 3 weeks in Japan it should be more than enough.
I'm most likely going by myself too... my friend who likes ayumi probably won't be able to afford it, so it'd be cool to meet some ayu fans who are going as well.