I can't find it at the moment, but there was this show where they explored different (and often radical) ideas. One of them was to build a massive landfill like 50km long, wide and deep (can't remember the exact size). Landfill is compressed and dumped into this massive hole could hold all the US rubbish for 100 years.

The title of the post triggered the memory of this idea. I guess digging really deep into the earths crust must also be expensive, but probably not as much as getting it into space.