I am looking to move some ETH from an exchange to a wallet for which I control the keys. I don't, however, want to download the whole blockchain.
Is there a good SPV client I can use?
Ethereum hasn't yet released features which would provide something like SPV. Instead of SPV it will be called Light Client and the protocol for this being developed is called "LES".
More information on the ethereum github wiki.
Jaxx by Kryptokit might be what you're looking for.