I agree that local stuff can be really useful - our local listings magazine folded a while back, and I never buy the local paper (owned by same company as Daily Mail) but there are lots of twitter accounts putting out news & events, and local councillors and so on do tend to use it to interact with people.
AchyFox - I don't think there would be a 'twitter classics' list anywhere, because it is such an ephemeral medium - something can be really funny in the moment, because it crops up within a minute of a piece of news or something on TV, but it won't really stand the test of time.
For example, watching the Olympic opening and closing ceremonies with half an eye on twitter was hilarious, as are things like the Eurovision song contest - that kind of thing is the only time I really use hashtags, which is one of the main ways you get to see tweets by people you don't follow.
A good way to start might be with picking a few people you find interesting from something like the Times Top 50 that comingintomyown mentioned, or this list of the 200 most influential people on twitter - everything from members of One Direction to some non-celebrities who are big on twitter because they are funny/interesting. Or the Telegraph has done a few things on twitter, e.g. 30 funny people to follow on twitter or even 10 dead people to follow on twitter. And of course MNHQ is on twitter and if you look at who they follow, you'll find a mix of mumsnetters, bloggers and other interesting people.
It tends to kind of snowball - you follow a few people, they retweet things from other people who sound interesting, so you follow them, and so on.