PLT OF LTT ACR ACFT INADVERTENTLY LANDED AT THE WRONG ARPT.

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WE DEPARTED FAYETTEVILLE; AR ENRTE TO JOPLIN; MO; WHICH IS AN APPROX 30 MIN FLT. ENRTE TO JOPLIN THE VISIBILITY DETERIORATED DUE TO FOG AND HAZE. WE CONTACTED CTR AND WE WERE CLRED DIRECT TO JOPLIN. SINCE THERE IS NO NAVAID ON THE FIELD; I ASKED FOR VECTORS TO THE LOM FOR ILS 13 WHICH IS APPROX 4 NW OF THE FIELD. I NORMALLY USE NEOSHO VOR AND DME TO LOCATE JOPLIN ARPT. THE NEOSHO VOR IS 18 MI S OF JOPLIN AND WAS OTS. CTR GAVE US THE WX AND TOLD US TO EXPECT VISUAL TO RWY 18 AT JOPLIN AND TOLD US TO RPT THE FIELD IN SIGHT. A SHORT TIME LATER; I SAW A ROTATING BEACON AND A LIGHTED N-S RWY. I TOLD CTR I HAD THE ARPT IN SIGHT AND WAS CLRED FOR THE VISUAL 18. WHEN I ENTERED FINAL; AGAIN I TOLD CTR; BUT WAS BELOW RADAR COVERAGE. I SWITCHED OVER TO JOPLIN TWR AND TOLD THEM I WAS ON FINAL FOR 18. THERE WAS NO RESPONSE. I ASSUMED THE TWR WAS NOT YET OPEN. I LANDED AND REALIZED I WAS AT THE WRONG ARPT. I WAS UNABLE TO REACH CTR; FSS; OR UNICOM ON THE FIELD. THERE WAS NO FBO OPEN. SINCE I HAD SUFFICIENT RWY; I DEPARTED AND CONTACTED CTR AND TOLD THEM OF THE SITUATION. CONTRIBUTING FACTORS: EXTREMELY POOR VISIBILITY; NAVAID OTS; NEW FO THIRD DAY ON JOB; NEW TO AREA; FLEW LONG SCHEDULE ON PRECEDING DAY FOLLOWED BY MIN REST. IT COULD HAVE BEEN PREVENTED BY ASKING CTR TO CONFIRM OUR POS RELATIVE TO THE ARPT AND LOOKING FOR MORE POSITIVE INDICATIONS OF THE JOPLIN FIELD.