This actually turned out to be pretty straight forward, though I am no programmer and I am POSITIVE that there is a better way to do this.
That being said, I simply did some math against the current date and the return from the getAlbumDate() function, using the Unix epoch format to make it simple. I chose to display a "NEW!" tag for any album updated in the last week, which comes to 604800 seconds. So, I inserted the php below into the album.php file.
<?php
if ((date(U) - getAlbumDate("%s")) < 604800){
echo "NEW!";
}
?>