I think that's obviously really, but piggy backing a large corp site doesn't necessarily make the domain name valuable.
Sure there are Twitter apps etc being made, but "BestTweet" is limited realistically to listing memorable tweets. And generally, people follow a person's channel.
That said it is short and catchy, and perhaps a site with "Best Tweets" could be profitable. But they are too few potential end users to be able to give a value, depends on their budget, project, and like of the name etc.
Get it visible on the market places for a year and either accept an offer or decide to renew for longer based on offers you get.