Currently when a user goes to SEDE they must first pick a site for which to run their query. Only then can they browse the available queries or compose one of their own.
Seeing that the queries are the focus of the site I think it'd work better if we allowed them to browse/compose queries first and once they have the query then allow them to switch what site they want to query on the fly.
So at http://odata.stackexchange.com/ users would see what's currently the queries page.
The Queries and Compose Query buttons are both visible on every page (just like SO's navigation buttons).
Once they select a query or hit the compose button I'm thinking they see a page that looks like this. We can switch the radio buttons out for something better looking if necessary.
We default to the SO database but if the user selects one of the others we save their preference for next time. When they click Run Query they get the results for whatever site they have chosen.
I know this messes with the routing scheme (and permalinks?), but fixes the confusing navigation issue on the non query pages and gets rid of the "Select a site" page/click they have to go through every time they visit the site.