I tried two different areas on TweetStats because they do two very different things and seem to be the easiest apps/site to use.
TweetStats is fun and easy to use. It lets you view the number of tweets in a month, see a cloud of what you've tweeted and see follower stats. I like how everything is straight forward and would be easy to present to someone. I'll probably continue using TweetStats just to keep track of what I tweet and to see what it looks like.
TweetStats Trends is also fun to use because it shows the different trending words of everyone on Twitter and you can see things like the top 50 trends of all time. It's fun to see what people think should be important or what they want to promote.
I think I'll continue to use the TweetStats site for the stats and trends. These could be handy to use in a library if your library has a Twitter account. You could keep track of how often you are posting updates about the library. It would also show you what you talk about the most so you could track that and see if it works for you or tailor it more to what you think people are looking for.
Overall an interesting site with two great components, stats and trends, that are easy to use and informative too.