If you provide a location in your Twitter profile settings, then following @topix_local will get you tweets about the location. To stop getting alerts, simply stop following @topix_local. This needs a city name in your profile settings to be effective so that it picks-up the hashtag (#city).
UPDATE: You won’t get very many Tweets using @topix_local compared to using TweetDeck and creating a column for #City. But of course, in TweetDeck, you will get everything with the city hashtag, whether it’s news or not.