Low reputation (too many years of lurking, sigh) so I can't yet comment inline, but I found the answer from @laktak to be the only one that worked as intended on Ubuntu 18.04 -- using tar -cjf site1.tar.bz2 -C /var/www/site1 .
on my machine resulted in all the files I wanted being under ./
inside the tar.bz2 file, which is probably ok but there is some risk of inconsistent behavior across OSs when un-tarring.