E120 FLC ACCEPTS VISUAL APCH CLRNC AND TURNS FINAL TO WRONG ARPT. FLC RECOGNIZES THEY ARE AT WRONG ARPT ON SHORT FINAL; EXECUTE A MISSED APCH; AND REQUEST VECTORS TO INTENDED DEST. PIC ACCEPTS RESPONSIBILITY BUT QUESTIONS ATC'S LACK OF INVOLVEMENT EXCEPT AT LAST MOMENT.

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DURING DSCNT INTO MKE; XPONDER #1 (PRIMARY) STARTED GIVING WRONG INDICATIONS TO ATC. READOUTS WERE BTWN 1000 TO 1500 FT LOWER THAN ACTUAL ACFT ALT. BROKE OUT OF A SCATTERED CEILING AROUND 3000 FT AND LEVELED AT 2600 FT AGL APPROX 15 MI FROM THE W COAST OF LAKE MICHIGAN. APCH CTLR ASKED IF WE HAD FIELD. CREW RESPONDED WE DID AND CONTINUED TOWARDS THE FIELD FOR THE VISUAL TO RWY 1L. ACFT WAS BEING FLOWN BY THE FO AND HE ENTERED A BASE FOR FINAL TO RWY 1L WHILE THE CAPT COMPLETED LAST MIN CHKLISTS. AS SOON AS WE TURNED A 4-5 MI FINAL IN A HIGH ALT; STILL 2600 FT MSL AND CLEAN CONFIGN; WE REALIZED WE HAD LINED UP AT THE WRONG ARPT; APPARENTLY RAC; WHICH IS APPROX 15-20 NM SSE OF MKE. CREW CALLED MISSED APCH AND TWR THEN GAVE VECTORS TO MKE. CREW REALIZED THEY WERE LINED UP AT WRONG ARPT WHEN HEADING INDICATOR AND RWY DIDN'T ALIGN; AND ALSO WHEN THERE WAS NOT ANOTHER PARALLEL RWY. ONCE THIS WAS NOTED WE DOUBLE CHKED ILS AND NDB WHICH WERE SET FOR THE CORRECT RWY. IMMEDIATELY I (CAPT) CALLED MISSED APCH AND ASKED FOR VECTORS FOR MKE. AFTERWARDS; NORMAL LNDG WAS COMPLETED AT MKE. CONFUSING FACTORS I BELIEVE WERE APCH HAD ACFT ON VECTORS STRAIGHT TOWARDS RAC. ALSO ONCE APCH CTLR QUESTIONED MODE C; CREW TURNED XPONDER TO A NON ALT RPTING MODE. I BELIEVE APCH MIGHT HAVE ACCIDENTALLY CONFUSED US WITH AN ARR INTO RAC BECAUSE VECTORS WERE TOWARDS BASE; FINAL FOR RWY 4. ALSO; CREW ACCEPTED VISUAL WHILE STILL 5-10 MI OVERWATER APCHING RAC. I BELIEVE DUE TO THE LOWER ALT READINGS ON MODE C; THE CTLR WAS GIVEN IMPRESSION THAT WE WERE LNDG AT RAC. WE AS A CREW FAILED BECAUSE WE ACCEPTED THE APCH TOO FAR FROM AN ARPT IN AN UNFAMILIAR AREA. AND; THE CREW FAILED TO XREF INSTS UNTIL AFTER TURNING A LONG FINAL WHICH WAS FOR THE WRONG ARPT. ANOTHER CONFUSING FACTOR WAS WHY WE WERE HANDED OVER TO TWR APPROX 25 MI FROM MKE WHILE ON FINAL FOR RAC; AND WHY WE WERE GIVEN CLRNC TO LAND SO FAR OUT? I KNOW FINAL BLAME RESTS WITH ME. I FEEL THAT APCH'S VECTORS AND TWR'S LACK OF AWARENESS OF OUR POS SHOWS A DEFICIENCY ON EVERYONE'S PART. ALSO WITH THE EMB120; THE BEFORE LNDG CHKS DIVERTED MY ATTN LONG ENOUGH THAT I DIDN'T REALIZE THE SIT; UNTIL WE HAD STARTED FINAL APCH. TOO MANY ITEMS TO DISTRACT BOTH CREW MEMBERS; ESPECIALLY WITH A RESERVE CAPT WHO IS A RECENT UPGRADE AND A BRAND NEW FO.