Browse.log on the Commserve is a good place to start.
EvMgrS.log on the Commserve generally tracks anything related to the GUI, so also good.
Note that it's not going to always be easy to find the information, many things will listed by ID intead of name.
If you actually get to the point of running the restore and want to check something, most iDAs will let you view restore history and resubmit the job if it is less than 7 days old.
Right-click, resubmit job will bring up a form with the details of the operation.