Across my kitchen doorway and the entrance to the storage room: cayenne pepper and cinnamon.*
Inside the storage room: a mixture of icing sugar and baking soda.
The method to my madness: the pepper and cinnamon are to keep the ants in the storage room (they're coming from the storage room, somehow) and out of my kitchen and laundry room. And baking soda is apparently lethal to ants, but they need to be attracted to it with icing sugar.
I'll tell you if it works. I might not tell you if I end up resorting to filling my home with toxic chemicals again.
* First I tried the pepper, and the ants were walking through it too easily. Then I tried cinnamon. Conclusion: cinnamon works better than cayenne pepper. The occasional ant still got through the cinnamon, but very few even tried. Other conclusion: try not to get cinnamon and cayenne pepper into a cut in your finger.