A B737-300 APCHING LGA EXECUTES A GAR TO AVOID WINDSHEAR. ACFT IS BUFFETED WHILE AIRBORNE WITH ROUGH AIR CONDITIONS UNTIL IT FLIES AN APCH IN THE OPPOSITE DIRECTION AND LANDS.

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PREFACE: LGA ATIS ABOUT 1 HR OLD. NO INDICATION OF FRONTAL PASSAGE AT OR W OF LGA. ALSO NO PRECIP AT LGA. POS: #2 ON ILS RWY 22 LGA BEHIND ACR 3 (JET) 4 MI JUST OUTSIDE OF FINAL APCH RWY 22. ACR 3 GETS WINDSHEAR AND GPWS ON 1 MI FINAL; GOES MISSED APCH. I WAS THEN CLRED FOR ILS 22 APCH RWY 22 LGA. I HAD MY FO (PNF) DECLINE APCH CLRNC AND REQUEST HOLD AND OR DELAY VECTORS. VECTORS AND CLB AND HDOFS. THEN APCH CTLR ISSUED HOLD CLRNC TO A VOR LESS THAN 2-3 MI AWAY! FO WAS FAIRLY NEW -- COULDN'T BUILD APCH IN FMC; A LOST SOUL -- SO I WENT INTO RAW DATA HOLDING (150 DEG RADIAL; 5 MI FIX; 10 MI LEGS AND L HAND TURNS). FO HAD HARD TIME FINDING AND IDENTING FIX. NEVER BEEN INTO LGA BEFORE. FRONTAL PASSAGE WX (NOT ON ATIS) BEATING US UP. 'WELCOME TO LGA AND NYC!' I THINK I DID OK IN RAW DATA HOLDING. WHO KNOWS? ONE TURN THEN APCH CTL ISSUED RADAR VECTORS TO START APCH (LOST FO STILL TRYING TO BUILD HOLDING IN FMC). ILS RWY 4; CIRCLE TO RWY 32 LGA. I THINK ACR A LEFT AND WENT TO ALTERNATE. ACR 2 BEHIND US; DOING SAME APCH. 2 MINS LATER ON ILS 4; CLRED FOR APCH; SHORT TURN-ON! STORMING AND MODERATE MIXED ICE; AND MODERATE CHOP. VISUAL WITH LGA 3 MI AT ABOUT 1200- 2000+ FT MSL STARTED CIRCLE TO RWY 31. POOR CIRCLING; TOO CLOSE; SO HAD FO REQUEST RADAR VECTOR FOR ANOTHER (CAN'T REMEMBER WHAT FO SAID). RADAR VECTOR TO SAME APCH AND IT WORKED OUT OK -- HVY RAIN AND MODERATE TURB ON FINAL RWY 31 LGA. HINDSIGHT: MANY MISTAKES OF MYSELF; FO; AND ATC. FRONTAL PASSAGE; ICE; LOWER CEILING; VISIBILITY AND TURB AND WINDSHEAR NOT ON ATIS ON DSCNT JUST PRIOR TO XX00L. GOOD DECISION NOT TO SHOOT ILS RWY 22 BEHIND ACR WINDSHEAR AND MISSED APCH. AFTER REQUESTING RADAR VECTORS AND OR HOLD AFTER 2 OR 3 DIFFERENT CTLRS THE TIME DELAY WAS SOMEHOW MISSED IN THE HDOFS; SO AFTER ONLY 1 TURN IN HOLDING; ISSUED APCH CLRNC AND RADAR VECTORS TO CIRCLING APCHS. EVERYONE WAS BEHIND AND OFF GUARD. I SHOULD NOT HAVE ACCEPTED CLRNC SO SOON OR EVEN HOLD CLRNC SINCE IT WAS LESS THAN 2 OR 3 MINS PRIOR TO THE DME HOLDING FIX. THINGS GOT WORSE SO I HAD TO SHOOT A MISSED APCH; BUT IF I HAD THOUGHT FIRST; THIS WHOLE THING COULD HAVE BEEN AVOIDED BY JUST REQUESTING A LOC RWY 31 APCH! WHY WASN'T LGA TWR USING IT? THEY DIDN'T KNOW THE WX SIT EITHER!