You are right, I just tried Astro and could not see the contents of /data
You should get root explorer, well worth the money.
Either that or you could use a terminal to copy the file. slightly harder.
Download Android Terminal Emulator (free) It might already be on Apex; run terminal emulator:
Make sure the bootanimation.zip file is on the root of your sdcard
-type
su
It should ask for root permissions, allow it. If the keyboard goes away, don't panic, just hold the hard menu button on the left of the hard home button. then type -
cp /sdcard/bootanimation.zip /data/local
Make sure you put a space between the "cp" and "/sdcard" and also "bootanimaton.zip" and "/data"
That should do it.
I believe to use the /system/media folder, you will need root explorer and do the "Mount R/W" before placing the bootanimation.zip file there. Astro won't be able to access it.