A BE76 ACFT LANDS AT THE WRONG ARPT IN IDAHO.

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BTWN BURLEY; ID; AND POCATELLO; ID (UNFAMILIAR AREA); EXPECT CLRED FOR VISUAL APCH (20+ MI). AFTER IDENTING ARPT; CLRED FOR VISUAL APCH RWY 21. LOOKED AT COMMERCIAL CHART ARPT MAP AND SAW SIMILARITY AND A LARGE '21' ON THE LONG PAVED RWY. CONTACTED TWR; RPTED DOWNWIND; AND FINAL WHEN CLRED TO LAND. LANDED AND TWR WAS HARD TO HEAR. STILL NOT KNOWING WE WERE AT WRONG ARPT; STOPPED AT WHICH APPEARED TO BE FBO. LOOKED UP. CARD IN WINDOW SHOWED WE WERE AT AMERICAN FALLS. REALIZED PROB AND DECIDED TO TAKE OFF AND CONTACT TWR. ATTEMPTED TO START L ENG AND IT REFUSED. I GOT OUT OF ACFT AND CALLED FSS ON PORTABLE PHONE AND ADVISED THEM TO LET CTR KNOW (AND THE TWR) WHAT HAD HAPPENED. TURNED ON ACFT RADIO AND ASKED PLT TO RELAY WE HAD LANDED. (HE TOLD TWR WE HAD PUT IT DOWN SOMEWHERE AND SEARCH HAD BEGUN BECAUSE OF THIS.) FINALLY GOT ACFT STARTED AND AIRBORNE. CONTACTED POCATELLO TWR AND LANDED. MEANWHILE; SHERIFF WENT TO AMERICAN FALLS. RPTED US NOT THERE AND SEARCH WAS STARTED AGAIN UNTIL THE TWR TOLD SHERIFF WE HAD FINALLY LANDED AT THE RIGHT ARPT. PSYCHOLOGICAL FACTORS INVOLVED DIFFICULT IFR FLT WITH SEVERAL AMENDED CLRNCS; MODERATE TURB; AND TSTM AVOIDANCE UNDER IMC.