If you power your project using 2xAA batteries (NiMH or alkaline), you don't need a regulator at all.
Another possibility is to use a lithium battery, with a series diode to drop the voltage below 3.6V.
Or, you can do much better than the regulator you have. The MCP1700 Low Quiescent Current LDO 3.3V reg has a quiescent current of 1.6 uA.