INSTRUCTOR AND STUDENT ABOARD A PA32 FIND THEIR DEP ARPT BELOW MINIMUMS WITH FOG.

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A LCL IFR TRAINING FLT WAS INITIATED ABOUT 1/2 HR BEFORE DARK; AND JUST BEFORE SUNSET. THE WX WAS CLR AND WAS IN A GAP OF ABOUT 3-4 HRS BTWN FRONTAL RAIN SYS. AFTER CONCLUDING THE TRAINING; WE RETURNED TO MILLEDGEVILLE; GA; TO CONCLUDE THE FLT WITH A GPS APCH. WE COULD SEE AREAS OF GND FOG AS WE APCHED; AND SPECULATED ON WHETHER THE LNDG COULD BE MADE OR NOT. ON SHORT FINAL IT BECAME OBVIOUS THAT THE LNDG COULD NOT BE COMPLETED DUE TO FOG. WE STARTED THE MISSED APCH AND TUNED IN TO THE MACON ATIS. IT RPTED CLR AND 10 MI VISIBILITY. WE PROCEEDED SW TO LAND AT MACON. A VERY FEW MINS LATER; THE ATIS CHANGED ITS RPT TO LESS THAN 1 MI VISIBILITY AND ONLY A FEW HUNDRED FT CEILING. AS PLAN C; WE TURNED TOWARDS ATHENS; GA; AND UPON TUNING THEIR ASOS; FOUND THAT ATHENS WASN'T A GOOD CHOICE EITHER. AT THAT POINT; WE CONTACTED ATLANTA APCH FOR ASSISTANCE. THE CTLR GAVE US SEVERAL ARPT CEILING AND VISIBILITY RPTS; AND CONFIRMED THAT WE WERE IFR EQUIPPED; AND CAPABLE; SHOULD THAT OPTION BE NEEDED. HE ALSO VERIFIED OUR FUEL STATUS; WHICH WAS 2 HRS 30 MINS. OF THE CHOICES OFFERED; GWINNETT COUNTY (LZU) WAS CHOSEN. THEIR ATIS RPTED 5 MI IN MIST; CLR BELOW 12000 FT. DURING THIS ENTIRE TIME; WE WERE IN VFR CONDITIONS WITH PATCHES OF FOG AT THE SURFACE. SEVERAL ARPTS WERE OBSERVED WHILE ON THE WAY TO LZU; BUT THEY WERE ALL AFFECTED BY FOG. THE ATIS RPT AT LZU WAS FOR THE TIME OF XA45; AND OUR APCH WAS AT ABOUT XB30. THE AGE OF THE ATIS RPT GAVE REASSURANCE THAT THE CONDITIONS WERE HOLDING AT VFR. ON FINAL; WE COULD SEE THE ENTIRE ARPT AND BEYOND. THERE WAS A SHALLOW; THIN FOG LAYER AT ABOUT 100 FT ON FINAL; BUT AT NO TIME DID OUR VISIBILITY DROP BELOW 1 MI. THE LNDG WAS SUCCESSFULLY COMPLETED. THE FAILURES (AS UNDERSTOOD AT THIS TIME) WERE: 1) RELYING ON LCL KNOWLEDGE OF THE PROBABILITY OF FOG. WE OFTEN HAVE FOG AT MLJ; BUT BEING BTWN 2 BANDS OF WX LED ME TO BELIEVE THAT THERE WOULDN'T BE FOG THAT EVENING. AND EVEN IF OUR LCL LAKE SYS CREATED FOG AT MLJ; THE LIKELIHOOD OF FOG AT ALL THE SURROUNDING ARPTS (WITHIN 50-100 MI) SHOULD HAVE BEEN REMOTE. 2) UPON APCHING LZU; I SHOULD HAVE ASKED FOR LCL IFR TO SERVE AS ASSURANCE THAT; SHOULD LOWER VISIBILITIES OCCUR ON THE APCH; WE WOULD HAVE BEEN 'IN THE SYS' AND LEGAL TO CONTINUE THE APCH. 3) WITHOUT THE IFR CLRNC; I SHOULD HAVE ASKED FOR AN SVFR CLRNC FOR ENTRY INTO THE CLASS D AIRSPACE AT LZU. #2 AND #3 WEREN'T VERY CLOSE TO MY THINKING PROCESS AT THAT TIME. AS IT TURNED OUT; #3 CERTAINLY SHOULD HAVE BEEN USED ON THIS FLT.