I didn't know places charged. I voluteer at the Juvenile Diabetes Reserach Foundation. It is a great program mostly volunteer run. 85% or more of their giving goes directly to research, so voluteers I vital. They have all kinds of areas, office, out reach, their walk, their Gala...
Schools can be a great place to volunteer as well, even if you don't have kids going there.
Some volunteer organizations do charge fees as an volunteer group known as auxiliaries. There are many other organizations that do not charge. Especially the small organizations like For The Child.