C152 INSTRUCTOR; WITH STUDENT; GOT CAUGHT IN UNFORECASTED WX MOVING OVER HOME BASE RESULTING IN MAKING A MISSED APCH AFTER DSNDING TO 600 FT ON A LOC AND AFTER BEING ADVISED BY ATC THAT THEY WERE 2 MI OFF COURSE.

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I WAS THE CFI ON A LCL TRAINING FLT VFR OUT OF SANTA ROSA; CA; SONOMA COUNTY ARPT. WE TOOK OFF AT APPROX XA30 WITH VISIBILITY AT 12 MI; SKY CLR. WE HEADED E FOR A 20 MIN FLT TO ANGWIN (2O3). LANDED; TOOK OFF; HEADING S TO SONOMA SKYPARK (0Q9). EACH SEGMENT WAS APPROX 20 MIN TIME. TOOK OFF FROM SONOMA SKY PARK BACK TO SONOMA COUNTY DIRECT AND I NOTICED THE WX MOVING IN FROM THE W. SANTA ROSA ATIS RPTED CEILING 2500 FT BROKEN WITH VISIBILITY 2 1/2 MI IN RAIN. I REQUESTED A SVFR CLRNC AND TWR RESPONDED WITH A DELAY OF 20-25 MINS DUE TO IFR DEPS AND ARRS. THEY SUGGESTED IFR WITH ZOA. I THOUGHT ABOUT THIS; AND DECIDED TO GET A LOC APCH FROM CTR; AS I HAD 1 NAV RADIO WITH NO GS AND WITH RPTED CEILING AT 2500 FT I WOULD BE UNDERNEATH THE CEILING AT ABOUT 2400 FT AGL AND PROCEEDED INBOUND ON A VISUAL. ZOA VECTORED ME AROUND A FEW TIMES FOR THE APCH AND HAD ME HOLD FOR A PRIORITY DEP (AIR RESCUE). AT COATI INTXN; USING 1 VOR; I IDENTED COATI AND ENTERED 1 TURN IN THE HOLD THEN CTR CLRED ME TO REINTERCEPT THE FINAL APCH COURSE AND CLRED ME FOR THE APCH. CTR TURNED ME OVER TO SANTA ROSA TWR. I MADE TWR CONTACT AND DSNDED THROUGH 2500 FT -- NO VISUAL; STILL IMC. AT THIS TIME; TWR ISSUED A SPECIAL RPT TO ME. I BELIEVE THEY SAID; 900 FT BROKEN OR OVCST; VISIBILITY 1 1/4 MI WITH LIGHT RAIN. I WAS STILL NOT VISUAL AND ABOUT 1 MIN OR SO LATER; I REALIZED MY LOC NEEDLE HAD A RED FLAG. I RECYCLED THE FREQ AND OBTAINED A FULL SCALE DEFLECTION (R NEEDLE). I TURNED BACK TOWARDS COURSE AND NEEDLE FAILED AGAIN. ABOUT THIS TIME; WE BROKE OUT OF CLOUDS AT 600 FT OR 700 FT AGL AND TWR NOTIFIED ME THAT CTR HAD US ABOUT 2 MI W OF COURSE AND SUGGESTED A MISSED APCH. I CONCURRED AND MANEUVERED FOR THE MISSED PROC. I REQUESTED THEN RADAR VECTORS TO THE NEAREST VFR ARPT (THE MISSED APCH IS LONG AND I COULD NOT AFFORD THE FUEL TO FLY THE WHOLE PROC WITH POSSIBLE HOLDS). THEY (CTR) UNDERSTOOD; BUT SAID THEY WOULD HAVE TO SEND ME S FIRST. I SAID I NEEDED TO GO DIRECT NAPA BECAUSE I WAS THEN THINKING I HAD 30-40 MINS FUEL. 'NAPA IS RPTING 3000 FT BROKEN; VISIBILITY 10 MI IN RAIN;' THE CTLR TOLD ME. I SAY FINE. I TOLD THEM THAT I WAS JUST SHORT OF DECLARING AN EMER. THEY ASKED IF I WAS. I SAID IF THAT'S WHAT IT TAKES TO GET PRIORITY -- YES. I DID NOT HAVE A NAPA APCH PLATE. THEY GAVE ME VECTORS TO FINAL VOR 6 APCH; FINAL APCH COURSE AND MDA. THE WX MOVED WITH US AND CEILING DROPPED TO 1000 FT BROKEN. WE BROKE OUT ON COURSE; ARPT IN SIGHT; LANDED; END. NAPA TWR HAD ME CALL ZOA AND I EXPLAINED THE ABOVE EVENT. WE FUELED AT NAPA AND WE HAD 30 MINS OF FUEL AFTER LNDG. TO PREVENT THIS FROM HAPPENING; A 180 DEG TURN IN BACK TO SONOMA SKYPARK WOULD HAVE BEEN BEST AND BETTER EQUIP.