Ooops, to answer your actual question, I find that setting a daily budget for renewing, and renewing throughout the day, everyday is best. My current daily budget is about a $1.
Also, traffic can vary from day to day, so it's difficult to determine when the best time is....
There is an app that will automatically renew your stuff for you based on Etsy traffic, though, it monitors views in real time and when views are up, it will relist for you. You can also set a budget.
http://www.etsy.com/apps/53113472/uncle-gravys-renewing-agent-updated