If you are committed to using all available batteries, my recommendation would be to put 2 groups in parallel, each group being a string of 4 in series. Then the output voltage would be 4.8 volts if you are using 1.2V batteries, or 6 volts, if you are using 1.5V batteries. In the former case, you can dump the regulator, because generally it is not going to be more accurate than the 0.2V difference, and it will also save you the energy that will be dissipated in it otherwise.
The recommended configuration delivers enough voltage while also maximizing efficiency in the use of available energy. I did the calculation. The exact result, assuming your fed circuit behaves like a large resistor R is:
T=(RU/E) (2r/R +1)/2
Where T is run time, U is the amh reserve of a single battery, E is the emf of a single battery, r is the internal resistance of a single battery.
By comparison, if you use a single group of four batteries in series, the result is:
T=(RU/E) (4r/R +1)/4
So, when r<<R, the recommended configuration will run twice longer than the second one, which is what we would expect.