If you are looking for Japan based exchanges, Bitflyer is the biggest. That'll let you buy up to 250,000 yen worth of Bitcoin (at time of writing about $2,250) each month with only a phone number or Facebook account. After verification you can buy more.
If you
really want to be safe with your Bitcoin though, I would try
LocalBitcoins. It's anonymous and lets you do cash transfers, so you could buy large amounts of money from a trusted seller. Unfortunately some people sell LocalBitcoin accounts with high trust sometimes, so the best thing to do is choose more than one account each quarter and exchange with cash since it's not reversible, which would make you anonymous and mean that you're not dealing with an exchange.