If you are willing to have the wallets of whichever cryptocurrencies you want to trade on your own computer, you can't go wrong with Shapeshift or Changelly. I have used both of these without a problem. The only issue with them is that not only do they not act as a wallet at all, but they also may have significant fees depending on which cryptocurrency you are trying to exchange since all of the trades have to be done in their corresponding blockchains. This means that if you are having to do trades often, it may not be the way to go.