BEECH 1900 FLT CREW LANDS AT THE WRONG ARPT.

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WE WERE FLYING FROM MKE TO RHI. WE WERE TALKING TO ZMP. WE REQUESTED THE ILS RWY 9 AT RHI BECAUSE THE WX RPT THAT HE GAVE US CALLED FOR SCATTERED CLOUDS AT 1100 FT. HE ASSIGNED US A HDG OF 340 DEGS AND CLRED US DOWN TO 4000 FT. WE STARTED OUR DSCNT FROM 11000 FT AND AT 5500 FT WE BROKE OUT OF THE CLOUDS. WE SPOTTED A BEACON FOR WHAT WE TOOK AS RHI AND TOLD CTR WE HAD A VISUAL ON THE ARPT. HE CLRED US FOR A VISUAL APCH INTO RHI AND TO CHANGE TO ADVISORY. WE PROCEEDED TO THE BEACON AND SET UP FOR RWY 27; SINCE THE WINDS WERE OUT OF 280 DEGS. AS WE WERE ON FINAL; ABOUT 100 FT ABOVE THE FIELD; I NOTICED THAT THIS ARPT DID NOT LOOK LIKE RHI. SINCE WE WERE ALREADY CONFIGURED FOR LNDG AND ALREADY COMMITTED TO LNDG; I THOUGHT AS THE PF; THAT LNDG WAS THE SAFEST OPTION. IT WAS CONFIRMED WHEN WE STOPPED ON THE RWY AND THE TXWY TURN-OFF WAS NOT THERE. THE CAPT TOOK THE FLT CTLS FROM ME AND TAXIED THE ACFT BACK TO THE RWY. WE TURNED AROUND AND PROCEEDED TO TAKE OFF FOR RHI. WE CALCULATED THAT SINCE WE ONLY USED HALF THE RWY ON LNDG AND WE WERE LIGHT; WE WOULD SAFELY BE ABLE TO TAKE OFF FROM THIS RWY AND BE CLR OF ALL OBSTACLES. AFTER LEVELING OFF AND PROCEEDING TO RHI I WAS GIVEN FLT CTLS BACK. I LANDED SAFELY IN RHI. SUPPLEMENTAL INFO FROM ACN 715074: DURING THE ENTIRE APCH I WAS TRYING TO REINFORCE VISUALLY THAT THE ARPT WAS RHINELANDER. SIMILAR SURFACE FEATURES WERE IDENTICAL TO RHINELANDER; RWY CONFIGN LIGHTING; GND FEATURES AND TERRAIN. THE ONLY DISCREPANCY WAS OUR DME STILL SAID 14 MI AT A CLOSER UNDETERMINED DISTANCE.