WRONG ARPT APCH AND LNDG WHEN AN EMB 145 FLC INTENDS TO LAND AT SBN; BUT INSTEAD LANDS DURING NIGHT OP AT EKM; IL. PIC LATER; IN CONSIDERATION OF PAX COMFORT; TAKES OFF FOR SBN; IL.

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WE WERE FLYING FROM PVD TO SBN. ZAU CLRED US TO 3000 FT; THEN TO 2100 FT; AND CALLED SBN AT XA00 AND 25 NM. IT TOOK A FEW MINS TO SPOT A BEACON AT 12 O'CLOCK POS. I SET THE FMS FOR THE ILS RWY 27 AT SBN FOR THE FO; WHO WAS FLYING THE ACFT. BECAUSE OF THE PREVAILING WIND AND SPD; WE HAD TO USE RWY 27. THE ILS/LOC RWY 27 WAS OTS AT THE TIME; AND CONDITIONS WERE VMC. ZAU ADVISED US THAT ANOTHER ACFT HAD LANDED BEFORE US. AFTER SETTING THE FMS; I TOLD THE FO TO USE IT AS A BACK-UP TO A VISUAL FOR RWY 27. I CALLED CHICAGO AND ADVISED HIM WE HAD A BEACON IN SIGHT. AT THAT TIME; WE WERE CLRED FOR A VISUAL APCH TO RWY 27; AND THAT RADAR SVCS WERE TERMINATED; SWITCH TO CTAF -- FREQ 118.9. I CHANGED FREQ AND ADVISED SBN TFC THAT WE WERE ON A LONG FINAL TO RWY 27. WE COMPLETED THE LNDG CHKLIST; I LOOKED UP TO FIND OURSELVES ON SHORT FINAL. ALL LOOKED NORMAL; WHEN I GLANCED AT THE MFD AND NOTICED THAT THE DISTANCE DID NOT MATCH. AS I CHANGED RANGE ON THE MFD TO VERIFY OUR POS; THE FO WENT AHEAD AND LANDED. AFTER LNDG AT EKM INSTEAD OF OUR DEST SBN; WE COULD NOT FIND ANYONE AT THE FIELD OR ANY LIGHTED BUILDING. THE WX WAS BELOW FREEZING. I HAD NO MEANS OF CALLING THE COMPANY. THE FO DID NOT GIVE ME ANY INDICATION HE HAD A CELL PHONE. WITH NO PLACE TO SHELTER THE PAX; I MADE THE DECISION TO TAKE OFF AND FLY THE 10 NM TO SBN; AFTER MAKING SURE ENOUGH RWY WAS AVAILABLE.