Hi Trevor,
Thanks for your interest in Omeka. Correct me if I'm wrong, but it sounds like you'd like to mash up some kind of map api with objects in your collection, to create an online exhibition. We currently haven't released a plugin to do that, but Omeka's extensible architecture makes it possible for you to create one. At CHNM we've been working on a map plugin, but I'm unsure on the specific timeline for its completion.
My assumption is that you're looking for something like this in the end:
http://anthemsonmap.googlepages.com/index.htm
- Dave