My design exposes two kinds of resources:
I would like clients to be able to request random images by their tag(s). For example
I've struggled myself with this issue. What we ended up implementing was an HttpResponseRedirect from, eg:
http://www.example.com/randomNewYorkImage
to a random New York image:
http://www.example.com/images/New_York/1234.
The first resource can be conceived as a random New York images dispatcher. This solution will load more the server, as it will be requested two resources, but it is as RESTful as you can get.
Edited: Plus, if you are caching, each image will be in the cache, and your server goes from sending an image to sending only the redirect, as the cache will intercept the second request, and thus alleviating your server load.