Solar powered Arduino project
The solar panel should not be connected to the batteries for the following reasons:  


Overcharging can reduce the life of the battery. 
If the output voltage of the solar panel drops below the battery voltage, then the battery voltage will feed into the solar cell.
If the battery is empty, the solar panel may charge the battery too quickly (with too much current) which can reduce the life of the battery.


Instead, you should use a battery charging circuit. Many off-the-shelf boards can be found at online &amp; local electronics shops. Eg This battery charger from Sparkfun. Some of these boards turn off the voltage when the battery voltage gets too low - to prevent damage from over-discharging the battery.

I would also be cautious about having an LED indicator for when the battery is low. This will drain the battery even further and can damage the battery if it over-discharges. Instead, have a LED on if the battery is OK - although this will cause the battery to drain quicker.  

As a rough guide, the Arduino UNO only requires 20mA to operate. Providing that your external circuitry doesn't draw much current either, you can charge the battery and run the Arduino at the same time. Perhaps, the LED indicator could indicate that the solar panel is charging the batteries.

As Dmitry suggests in his answer, using the low power modes when on battery alone reduce your power consumption and hence increase the life until the battery goes flat.