GA SMA FAILED TO EXECUTE MISSED APCH PROC AT POINT INSTRUCTED BY ATCT.

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WE HAD JUST COMPLETED THE ILS 23 TO CUYAHOGA COUNTY AND WERE BEING VECTORED FOR THE LOC BC 5; ALSO INTO CUYAHOGA COUNTY. THE ACTIVE RWY WAS 23. MY STUDENT WAS HAVING GREAT DIFFICULTY IN MAINTAINING ALT (+/-200') AND HDG (+/-2- DEGS). WHILE VECTORING US FOR THE APCH; ATC ISSUED TO US SEVERAL TFC ADVISORIES. AS SAFETY PLT; I WAS CONCENTRATING ON LOCATING THE ACFT. MY STUDENT WAS SETTING UP FOR THE APCH IN THE MEANTIME. BECAUSE OF HEAVY TFC CONGESTION; THE TWR TOLD ME TO INITIATE THE MISSED APCH 5 MI FROM THE RWY; AND MISSED APCH PROCS WOULD BE ISSUED AT THAT TIME. AT WHAT I BELIEVED TO BE THE 3 MI POINT; I TOLD MY STUDENT TO MAKE A MISSED APCH. TWR THEN INFORMED ME THAT I WAS MUCH CLOSER TO THE ARPT THAT 3 MI. LOOKING BACK AT THE SITUATION; I SHOULD HAVE NOTED THAT THE MILEAGE FROM THE FAF TO THE MISSED APCH POINT WAS 4.5 MI; AND THAT THE MISSED SHOULD HAVE BEEN INITIATED SOON AFTER PASSING THE FAF. I WAS; HOWEVER; CONCENTRATING ON THE NUMEROUS TFC ADVISORIES. ANOTHER FACTOR WAS MY UNFAMILIARITY WITH THE NEARBY; BUT SELDOM-USED; ARPT (SELDOM USED BY ME). I ALSO BELIEVE THE LCL CTLR COULD HAVE ISSUED A VERBAL COMMAND TO EXECUTE A MISSED APCH. THIS WOULD HAVE ELIMINATED SOME OF THE GUESSWORK.