If you ask me, the safest places are exchanges, but if you are looking for a secure wallet without joining the exchange, I can recommend https://www.myetherwallet.com/, it has never been stolen and has a super protection strategy. 
Exchange is not the best wallet. The best example here is Mt.Gox, Cryptopia, Bithumb and many exchange that turn in to scam. Its a bad decision to leave your money on a wallet that you didnt own the key. But at some point, there are exchange that is safe to store funds like binance and coinbase because they are compliant to the law.
Practically speaking exchange is most convenient wallet if you are a trader but not the safest. Safest wallet is the one that you holds private key or a hardware wallet.