Use the --directory option:
tar czf ~/backup.tgz --directory=/home/username/drupal/sites/default files
Hi I've a better solution when enter in the specified directory it's impossible (Makefiles,etc)
tar -cjvf files.tar.bz2 -C directory/contents/to/be/compressed .
Do not forget the dot (.) at the end !!
cd /home/username/drupal/sites/default/filestar czf ~/backup.tgz *