What kind of volunteer opportunities are available for young people?

Call 211. They are the experts in non profits in your area. Volunteer at the local food pantry, soup kitchen, domestic abuse shelter, or homeless shelter. Read at the library, have a story hour. Read at the local hospital in the waiting room. Help at the animal shelter or humane society. If you can't do that; have a food drive; "Oodles of Noodles" is a pasta drive that is usually very successful for the food pantry. Collect new toothbrushes and hairbrushes for the domestic abuse shelter. Collect blankets, hats, gloves for the homeless shelter. Collect used blankets and towels for the animal shelter. The need is great; the opportunities are endless.

Library, Nursing homes, animal shelters, hospitals, food pantries, Tutoring only through the school

This might be out of the question, But you could volunteer out at a local charity shop? or At your local church? or This is kind of random, but you could babysit. Which isnt really volunteer work but its with kids.

I volunteer at a retirement home. What I did was to go on google and type "retirement homes in yourcity, your state" and then call to ask if you can volunteer :) its really fun to help them you can also try the local library or join leo club if your school has it

Search for nursing homes near your house using Google Maps "search nearby." Then just call them up and ask about volunteering. You could try to find tutoring work through a community center or a library.