This design looks reasonable, but I would like to do two changes:
1. keep the LEDs on while AC is there, and dim the light to some extent (LEDs remain on with battery power) and light up a warning LED when AC is out.
2. I don't like the 1000uF capacitor in line, since this circuit is meant to be working for long time. Will you recommend some AC-5V DC regulators ( say 5-20VAC input optional)?