As opposed to Duke, Vanderbilt does not have anything that approaches TLC. They do have a Center for Teaching, which seems analogous to our Center for Teaching and Curriculum (CTC). They offer a program similar to TATTO called TAO. They offer workshops on teaching, working groups on different issues, a teaching certificate program, and a Future Faculty Preparation Program. Both of these last two seem useful to me as far as filling a potential gap that Emory has (a GSAS-wide initiative beyond TATTO to improve teaching and to assist students with professionalization).
What they don't have is much in the way of training on technology. They do have a page on the Center for Teaching's website that is dedicated to an overview of teaching technology. The page has a number of resources, such as articles and book reviews. Unfortunately, most of these are far out of date (publication dates of 2001 and 2000 abound). The most useful things on the page are links to a second series of pages on things like class management software, online writing, and podcasting. These, however, turn out to be little more than FAQs. While they have some useful information--particularly the one on clickers--there is nothing about further training.
Further searches for centers of instructional technology and the like have turned up nothing. One thing I did find, however, is VUmix: Vanderbilt's music services for the school community. They can get, for example, Napster accounts and download an unlimited amount of music for $2/month. I wonder how this would affect their iPod ratios on campus since Napster only works with players that can handle WMA with DRM (i.e., almost every brand except for Apple). You can, of course, stream the music on any computer. If you're feeling left out of the good times and low-cost music, then you might want to check out Ruckus. It's a free subscription for all college students. The music is supported by advertising and can only be streamed. If you want to take it with you (on mp3 player), then you can pay $20 for a whole semester of this privilege. Of course you, again, need to have an mp3 player that is PlaysForSure capable. iPods need not apply.
In any case, my verdict regarding Vanderbilt's TLC capabilities? They don't seem to have anything like this. Nor do they seem to have a center of any kind that offers training to students or faculty on technology. I've placed a call to their Center for Teaching to try to get more information, but the appropriate administrator hasn't returned my call. Look here for edits in case I get more.