I have run Cygwin setup using a handful of different repositories, but certain programs appear to be missing from from the ones I have tried so far. I am specifically looking for tee and svn.
Which repositories/ mirrors are complete?
You can use the Cygwin Package List to find the appropriate packages.
The latest version of Cygwin includes /bin/tee as part of coreutils.
And svn aka Subversion is found in the self named package.
If you're not finding these packages listed in your mirrors, you're not running the latest version of Cygwin.