Run barebone arduino on 3Volts battery
You can connect the 3V worth of AA batteries directly to VCC of the ATMEGA, and either use an external 8MHz oscillator (crystal or ceramic, either one works) or you can even use the internal RC osscillator with a CLKDIV2 to make your clock speed 4MHz which will work all the way down to 1.8V volts. You can also use CLKDIV settings on the external oscillators if you wanted. These options are all in the "Fuse" settings which when working with AVRs you must become familiar with. There are multiple tutorials on how to set and read fuses online, so you should be okay with some time spent researching. 

This is the chart from the ATMEGA328P datasheet (page 316) showing the VCC voltage versus acceptable frequency of guaranteed operation. 



You can hook up the batteries to VCC pins of the microcontroller directly with just a power decoupling capacitor to help during digital "on/off" cycles and other forms of power spikes. Here is an example of how I do it. In your case the power net label "VCC" is literally the battery +pos terminals, and the "GND" net label is your battery -neg terminal.



good luck!