Using AA batteries to power Arduino and GPS unit
I suggest using 6 or 8 AA's (eg 6 alkalines or 8 NiMH) and a  MP1584EN DC ­DC Power Stepdown Buck Converter (about a dollar on ebay, 1.5 to 3 times that on Amazon).  Note, the hole pattern does not match up with breadboard spacing: 

The batteries would tie in via a couple of diodes (preferably Schottky), as shown below.  When the 12 V supply is off, the converter would be powered by 9.6 V from eight rechargeable AA's.  When the  12 V supply is on, no current is drawn from the AA's.  The converter output should be adjusted to 5V before being connected to the Nano or other devices it powers.

Using a buck regulator has two advantages vs a linear regulator: battery current is lower (allowing the battery pack to be more efficient as it discharges) and less energy is wasted as heat.

Note, it might make sense to remove the power LED from the Nano, to save 3 to 5 mA of current.







simulate this circuit &ndash; Schematic created using CircuitLab