Where does yum save the RPM files it downloads?

I believe what you are looking for is /var/cache/yum/<repo>/packages. This directory is expunged during package cleanup.

You can search for a file by name with the find command. An example: find / -name 'package.rpm' Wildcards are supported. find -name 'package*.rpm'

I verified today that on RHEL 6.7, the files are stored in /var/cache/yum/x86_64/6Server/rhel-6-server-rpms/packages/.

It is also worth noting that the plugin downloadonly is included in RHEL 6:

# yum install yum-downloadonly
Package yum-plugin-downloadonly-1.1.30-30.el6.noarch is obsoleted by yum-3.2.29-69.el6.noarch which is already installed