Wow! A 3 year plan to stay in Japan for 3 weeks?
I'm just glad you're not planning a 3 year stay. You'd probably be in your 50's by the time you buy that plane ticket.
You can find a business hotel in Tokyo for around 5500 yen a night. Toyoko Inn is a popular chain and if you become a member, you can get an even better deal on extended visits.
Of course things could change a lot in 3 years. The yen could be worth something different, the cost of living could go up, the chain could have gone under, etc.