LED Poster configuration
From the link you have posted it's not possible to be 100% sure of the forward current, but I'm going to guess they would be good for 20mA and still visible at 10mA. With that in mind...

The forward voltage of the LED is around 3.3V - three AA batteries gives 4.5V maximum. Therefore with one 3xAA pack you would have to wire this circuit 60 times in parallel to the batteries (I have shown this twice below - I really don't have the time for 60!). I have conservatively chosen the current to be 10mA, which should be enough for this to be visible.







simulate this circuit &ndash; Schematic created using CircuitLab

This will be a big pain in the butt wiring-wise, and not particularly efficient. Run time will be in the region of 4 hours though, which is nice.

An alternative, which reduces the amount of wiring would be to use 2x 3AA battery packs in series. Now, at a total of 9V we can't really get away with 3 LEDs in a row (3x 3.3V = 9.9V > 9V), so we'll be stuck with two, but it means you have less wiring to do. See the schematic below (this time 30 repeats would be required - again, I only show 2).







simulate this circuit

The current this time is around 11mA per LED (due to there being fixed basic resistor values and 240 Ohms not being one of them) but the overall effect will be similar. Run time will be around twice as long this way, as you might expect. You could reduce the series resistors down to 120 Ohms and get brighter LEDs, but drop back nearer the 4 hour mark for battery life.

There are other options such as using a boost circuit to increase the voltage from the 4.5V battery pack to around 12V and run parallel strings of 3 LEDs, but I think the circuits I have shown probably fit your skillset and motivation best. If it were me, I would plump for the second option.