My preferred Twitter client is Twhirl and it has a stored search tool but it does not do advanced searches. For instance I do not want to know what is happening on the highways and in the restaurants of Winchester, VA, USA. I want to see Tweets about Winchester, Hampshire, UK.
Twitter Search allows me to do this but I could not see a way to store the search like a group in Tweetdeck for instance. I could save it as a favourite in Firefox or IE, I suppose.
Then the obvious hit me between the eyes, store them in a MindManager map. I can have a private one on my desktop and publish the general ones for other to use on a web page.
This is my starter for ten of predefined Twitter Searches on a MindManager map.