There is no such thing as a fool proof system. They will always be able to produce a bigger fool.
First, I would make sure it has a gasketed access cover. If you build more than a few, some WILL fail, and you would either have to throw the whole thing away or just accept that you didn't need it in the first place.
Given those two thoughts above, you want to power a 3V, 20mA LED - 30 of them. That is 1.8 watts of output, or somewhere in the range of < 1 amp. Assuming you have current limiting resistors, that could easily take another watt of output power for full brightness, so figure 2.8 watts OUTPUT. (Current regulators could help that a bit, but not linear current regulators.)
I don't know the exact efficiency of any battery system, but I do know it is not 100%, not even possible. Let's figure you get only 2/3 of the energy back. That means you'd need to deliver 3.73 watts, we'll round that up to 4 to keep it simple.
You must now specify how long you want these LEDs to remain lit. One hour? A long winter's night after a cloudy day? Take your number of hours multiplied by the 4 watts of output and that gives you some idea of how much energy storage you will need.
I'd guess to last half the night after a cloudy day you'd need about 40 watt-hours of energy stored. You'll need to adjust this to taste. The type of battery you use will determine the actual voltage stored and will likely influence the final design of the LED wiring.
If we for now figure we'd need 1 amp and maybe 10 hours of run-time, that would mean a battery rated at 10 Amp/hours. That's a fairly big battery that could cost $25 or more, and if we figured needing a full 10 hours of charging time from a solar source, the solar battery would have to be able to deliver at least a few volts above the battery voltage at 1, or more likely 2 amps of charging current to account for the inefficiencies and clouds. I'd GUESS 6 volts at 2 amps or a 12 watt solar battery at least. The desired number of hours of illumination greatly effect the size of the solar battery.
These are all estimates based on my guesses as to the performance desired for this design. If you were to provide specific numbers then the design could be specified more accurately.
In the end, it is far more economical to cover the thing in those cheap plastic retro-reflectors of assorted colors.