Knowing when your followers are online (and seeing your tweets) is very valuable as you craft or evaluate your Twitter strategy.
With all the noise coming from the hundreds or thousands of users that your followers are also following, your tweets need to be front and center when they are looking at their feed.
I recently found a freemium Twitter app called Tweriod that should help. The free version breaks the week down (weekends versus weekdays) and graphs out when your followers are online. It even graphs out when your @replies came during the day to show when the best time is to expect a mention.
One warning is that it takes about a day to generate a report. They email you when the report is ready.
Try it out and let me know what you think!