The short answer to this question is – it depends. The best time of the day to tweet is whenever the tweet will get maximum exposure to your target audience. So the best time of the day will depend on:
Where your target followers are based: if you hope to gain followers in the US then don’t tweet between 9am and 2pm UK time as America sleeps . . . and
The target response: if you want your Twitter followers to do more than simply retweet, then consider what response you expect. If you are a café wanting more breakfast traffic, then tweet about special offers before 10 am etc.
One way to find out the best time for you to tweet is to repeat your tweets and check. Guy Kawasaki (@GuyKawasaki) in his blog suggests taking your most popular tweets and posting them again three times, eight to twelve hours apart. His theory is that the volume of tweets is so high that people don’t notice repeat tweets. You can then use Google Analytics to check when people either clicked a URL shortener or came to your website from Twitter. A warning - Do this too often, you’ll start to look like a spammer and people will stop following you!
Another option is to use Tweriod - a free twitter tool that lets you know the best time to tweet based on your followers’ profiles.
KissMetrics have produced a brilliant infographic demonstrating the relationship between social networks and timing. This infographic, sadly for us in the UK is based on US data, suggests that the best time to Tweet, if you want retweets, is 5pm as 6% of all retweets occur around 5pm. However, if you want people to click through to your website, then try either at noon (around lunchtime) or 6pm (getting home from work). US data or not, this makes sense. It also says that the best days to tweet are midweek or at the weekends; Monday is a slow day in the twittersphere.
The trouble is that if everybody then tweets between 5pm and 7pm, you have to be doubly engaging to ensure your tweet gets noticed amongst the torrent of others!