Is there a direct train to go from Venice to Nice or Monaco?

No, there is no direct train any more. It's been a few years since the night train from Venice to Nice was cancelled unfortunately. You can find the various train options here: a href="http://www.trenitalia.com/cms/v/index.jsp?vgnextoid=ad1ce14114bc9110VgnVCM10000080a3e90aRCRD" rel="nofollow"http://www.trenitalia.com/cms/v/index.js…/a The easiest options involve train changes in Milan and Ventimiglia and take 8 to 8.5 hours.