I want to make a JavaScript PhoneGap app being able to store information, like log in data or for a savegame, but obviously I'm not able to write into files with JavaScript ansd since this is supposed to work offline I am also not able to run a server script that manages it for me. I'm pretty sure there is a way to do this and I'd be very thankful for your help!
You can use local storage. Local storage only stores strings, so you'll probably want to serialize JSON when saving to local storage. See is a breakdown of local storage size by browser.
var myData = { foo: "bar" };
localStorage.setItem("myData", JSON.stringify(myData));
var retrievedDataString = localStorage.getItem("myData");
var retrievedData = JSON.parse(myDataString);