[GoNative]

Y300,000 a month is not bad money but you're hardly going to get rich anytime soon if you actually want to have much of social life. My wife and I each earn more than that and live in a cheap region of Japan (rural Hokkaido). We own our house and car so have no debts at all and we would save more than what you are looking to each month but it is generally easier to save when you have 2 incomes.
I would think in bigger cities like Tokyo or Osaka you'll be able to live a reasonable lifestyle on that sort of money but saving a 1/3 rd of it after taxes and living expenses will not be easy, especially if you also had a car to run.