curl -u USERNAME:PASSWORD -d location="Arlington, VA" http://twitter.com/account/update_location.json
You can even use GET, which means bookmarkable location settings (similar to FireEagle)
By extracting this away to Twitter proper, it means any application can set this information how they want, and have it updated in the user's profile. One thing that is lost is the 'home' location of that user as their profile potentially becomes very temporal.
FireEagle as the central store is a good option, however it is just one location store and Twitter's location will no doubt serve as the centralized location store for a number of new applications. As more social or personal applications gain location storing and sharing support, there is a question of how synchronization between these services will easily happen.
I don't want to have to set my location in multiple services. This is the same problem that troubles social bookmarking sites such as del.icio.us and magnolia. This may become especially problematic if there were automatic updating services that detected a change in FireEagle and then updated your Twitter location, and vice versa - which then updates FireEagle from Twitter. Perhaps causing an implosion of the GeoWeb.