Why do you say this? When it comes to exchanges they really look like one of the most secure to me. Poloniex looks decent to, and if you have problems with fees at coinbase, you could always try to use Gdax. It belongs to coinbase as well, but at least you can trade your coins to fiat, so you can't really complain about fees here, because it's all about the price you manage to get. Also, they only charge 15cent or something like that for a bank withdrawal, and right now I think it's hard to compete with that.

Anyway as for ways to secure your bitcoins, and although I like coinbase, I would recommend you to keep your coins at a hard wallet (trezor or ledger), or at least in desktop wallet like electrum. For me these are the most secure options for holding, since they are reliable and you have your private keys, and that does not happen on an exchange.