Coincheck is Japan's answer and successor to Mt Gox.
A decent exchange that is seeing high volume on Japans warming relation to digital currency. Fees are low with an extra surcharge for withdrawing your Yen quicker and a trading fee that encourages orderbook liquidity with with maker taker model.
The user interface is east and intuitive to use with its support for foreign users.
Every single transaction is traceable and irretrievably stored in the blockchain.
Your coins and deposits are available and tradable 24 hours a day, 7 days a week.
The registration is free, depending on the provider there are different fees for the trade.