Sweden's answer to this question is to convert them to waste-to-energy plants. See the link below.
When I went on a study tour to Sweden and Denmark, I was fascinated to see how they were using waste-to-energy not only to deal with waste that couldn't be recycled but also to create heat for nearby households as well as using this thermal system as a way to store excess energy from wind power at night. These are amazingly clean plants, not like the horrid incinerators the US built decades ago.
It helps that they didn't build these plants in the middle of no-where so they can get the heat where it's needed. In Copenhagen there's a powerplant that doubles as a ski slope! But in the US we could at least keep coal-fired power-station jobs and reduce landfill waste while the waste heat can keep the plant going.