find a file within a tar.gz archive

How about just:

$ tar tf archive.tar.gz | grep foo

Mount the archive as a directory. You can do it with the AVFS filesystem, which allows you to access any archive as a directory whose name has a trailing #.

mountavfs
cd ~/.avfs$PWD
find archive.tar.gz\# -name '*foo*'

I think it works with no pipe and grep.

like this: tar tvf archive.tar.gz "foo"

as this way, globs will also work.

tar tvf archive.tar.gz "*.foo"