Staples gives you $2 per cartridge, but you don't get cash. You get Staples Rewards, which you have to spend at Staples.
I collect used catridges and toner bottles from work, turn them in at Staples, spend the Staples Rewards on stuff I need at Staples, and donate an equal dollar amount to a local school.
There are several companies that will give your school cash for your used printer cartridges, but it might be a lot less. Maybe twenty-five cents for an inkjet cartridge. Some cartridges are worth more than others.
One of them was Cartridges for Kids. I can't remember the names of the other ones.
Try calling the schools in your area. You might find that elementary schools are more active in doing this than middle schools or high schools.