After a fresh install of Piwik 1.12, I deleted my first site, and now I get an error every time I log in unless I manually change the site ID in the query string:
The requested website id = 1 (or its property timezone) couldn't be found
Piwik shouldnt let you delete the site from UI. If you deleted from the DB, then it's normal you get error message. Simply re-create in DB.
That's how I deleted it - from the UI.
Can you reproduce this problem in 1.12 ? when I have only one website I cannot delete it from the UI (we prevent this so the user doesnt break her piwik).