How close is a pilot allowed to get to a runway without landing clearance?
From the Pilot/Controller Glossary:


  CLEARED  TO  LAND−ATC  authorization  for  an aircraft to land. It is predicated on known traffic and known physical airport conditions


A clearance to land is exactly that: a clearance to land. A pilot without landing clearance hasn't violated ATC instructions until their aircraft has, in fact, landed. So the answer to how close you can get is: anything that isn't touching the surface.