This is one of the glaciers in the south where you can quite easily get close to.

From the main road you have to drive a quite bad gravel road. Just go slowly and you'll be fine. Once you get to the parking lot, you are already very close to the glacier and the glacier lagoon and it is just a very short walk to enjoy the view.

I don't think there's any other glacier tongue where you can get closer to (without a tour company).