My smartphone reports my location to Google (to G+ and to the Android Device Manager). I'd like to read that location from a website/program to plot my location.
I could use another app on my smartphone doing extra tracking but that tends to drain the battery quite a bit (having two apps do the tracking).
Since Latitude was deprecated I can't seem to find a replacement.
As part of Android Google is offering a location API. However, it sounds like you are looking for some kind of personal web API where you can get access to the location already sent to Google. I'm quite sure that it doesn't exist and that Google has no plans of reintroduce anything like the old Latitude API.
I don't know what you are trying to achieve, but have a look at Google Account Activity. There you can export your location history manually.