I found the Dark Sky API to be interesting. It has data ranging from more basic things like temperature to the more specific, like moon phase and wind direction. There's a lot of fun stuff you can do with weather predictions and history, but I personally like that there is data available on sunrises and sunsets. It would be cool to make something that shows what the sky might look like in a specific time and location using gradients.
As far as politics, this API requires that you credit it somewhere on the page and it costs money after the first 1,000 API requests per day. I'm not sure whether that is a lot of requests or very few.