It is all about what your need is at the moment. If you access a public API, and you do not need to keep any records about user interaction with that API, you can just dump it on the client side and save up on server load. For example, if you want to put some Twitter feed in your UI, I see no reason to route this on your server, unless you want to filter that feed in some way.
If the API you call requires tinkering with the response or a special kind of request, then it belongs on the server.