What's the best way to phrase "没事是......做什么?" in english?
Do you mean “没事…做什?" If it is the case, then  没事 is short for '没事要做 (without thing that has to be done); or 没事發生(nothing has happened) 


  没事 means 'for no reason' or 'with no purpose' in this structure.


For example: 

"没事回來做什?" (for no reason, come back for what?/ why come back for no reason?)

"没事去看醫生做什?" (for no reason, go to see the doctor for what?/ why go see the doctor for no reason?) 


  It should be' 没事...作什', but '没事...做什?' is also valid because 做 is the modern counterpart of 作 in classical writting for the verb 'to do'