How to drive dozens of LEDs from an UNO R3 for a Christmas project

If he is just turning on and off groups of led's then why not just use a few cheap BJT transistors?
32 led's x 20ma = 640 ma <that's cheap 12v wall-wart territory.
break that into a few groups and he does not need much in the way of size to run them.
there are tons of cheap and easy to use bjt's out there.

if he wants to get fancy then shift registers would work better.

cat6 here is a handy tool for figuring out parallel/series chains of led's
http://led.linear1.org/led.wiz