To be slightly flippant: we get even more valuable information out of garbage dumps.

People usually bias their writing towards what they consider to be important information. And they leave out what they consider obvious context.

So we have a lot more information about battles and kings, then about daily life.

People are less biased towards highfalutin in the ways they produce garbage.

This is a very wise observation. The most important things are always the ones we think are so obvious that we don't mention them.

Battles and kings are not garbage.

No, but all the ancient historians wrote about battles and kings, so we have that info all written up already. Very few of them wrote about the life of the average peasant, so to find out about that, one of the richest kind of archaeological sources are literal garbage dumps: https://en.wikipedia.org/wiki/Midden

Whenever I hear people complain that our digital media won't leave much for future archaeologists, I always think of our enormous output of plastic, metal and glass garbage.

I was talking about literal garbage dumps. They are incredibly important for archeology.

Battles and kings and things that seem important when they are current, but aren't as interesting in a few hundred years as insight into daily life.

Kings are definitely garbage.

Other places that tend to provide this sort of information are tax records and wills, both of which tend to be somewhat likely to survive. Even if you can only see tax laws it can tell you a lot about how the society fitted together.