Tweriod is a free tool that runs an analysis of your followers (1000 for free plan) and gives you the best time to tweet to get maximum exposure. The last 200 tweets of each person are analyzed for activity.
The report is sent via email link and once viewed you can also click to adjust the times in Buffer for scheduling tweets. This two step process should get a few more eyes on your tweets.
They do have paid plans that include a monthly subscription and a one time report for only $5 USD. The maximum amount it can analyze is 5000 users which I presume is due to the API calls necessary.
So get to analyzing and see your best times to tweet!