If I use either Mist or MetaMask, I get the error message:
Unable to connect to http://localhost:8545. Invalid JSON RPC response: ""
How can I connect to the Remix localhost?
You're waiting for the Remix team to add support. Currently they only support local nodes running, but marked the issue as "soon" on October 4th:
I haven't actually used Mix, the Dapp IDE myself, but based on their documentation, and that error, it looks like it requires a local node running, and does not take advantage of an injected web3 API, the way Mist and MetaMask provide.