Reuse egg cartons.
I save all my egg cartons. I try to always get paperboard egg cartons as well, since styrofoam is so bad for the environment.
Egg cartons are great to use for learning and art projects, dying eggs, and for seed planters. I use them all the time in the daycare. Here are some great ideas for egg carton projects from my preschool Pinterest™ board:
https://www.pinterest.com/dcmom70/preschool/
Because egg cartons are not recyclable, reusing them is the best option. If an egg carton has residue inside of it, then I tear it up and put it in my backyard compost bin. But if it is clean, it goes in the egg carton stack to use later.
If you do not have kiddos at home, then see if nearby preschools would like them for projects. Anything that keeps them out of the landfill would be a better option than throwing them in the trash.