What should I do with leftover sulfuric acid from a sump pump battery backup?
If you can not find someone to take care of the acid for you, it is possible for you to dispose of it yourself.  this page which references batterycouncil.org which most discreetly describes the process outlined here that states:


Gather together all the acid you need to dispose of and put on some sort of concrete pad. The high acidity may harm grass and soil, so try to do this in your driveway or on the patio outside. If you have batteries to dispose of, pour the acid out of the battery into a plastic container that will not break down in acid. If you are unsure, pour just a little in the container and see if there is any reaction before emptying the whole battery.
Use rubber gloves and goggles anytime you are dealing with highly concentrated acids. Acid is harmful to the skin if exposed and especially to the eyes. If concentrated acid touches the skin, thoroughly wash the skin for five to ten minutes and then sprinkle with baking soda to neutralize any remaining acid.
Fill a larger container half full of water. Slowly add some of the acid that needs to be disposed of and stir gently. Slowly add the baking soda, one tablespoon at time. The solution in the container will bubble and foam as the baking soda neutralizes the acid. Continue to stir as you add each tablespoon full. Once the bubbling and foaming is complete, test the solution by adding another teaspoon of the baking soda with stirring to see if any more reaction occurs.. When the reaction is complete, wash the solution down the drain and refill the container half way with water.
Neutralize all the acid in the same manner as Step 3. Pour the neutralized acid down the drain. Follow the neutralized acid with lots of water. Continue to run the hose for five minutes after you are done and then turn off the water.