There is no difficulty in finding a place to volunteer. Kentucky Humane Society has a great program, just call them. They have classes to help get you started. Metro Animal Services is always looking for volunteers. Animal Care Society, a no kill shelter, is looking for volunteers. GRRAND, the golden retriever rescue always needs walkers for those not in foster care yet.
Actually, you can contact any through email at their websites. Search "animal shelters" in your area, or the name of the organization.