FLC OF A B737-300 BECAME DISORIENTED DURING A VISUAL APCH RESULTING IN APCH CTLR ASSISTING THEM IN CORRECTING THEIR HDG FROM THE WRONG ARPT APCH.

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DSNDING ON THE MARLIN 4 ARR INTO FLL (APPROX 13 DME NE OF FLL VOR); THE APCH CTLR ASKED IF WE HAD A VISUAL ON THE ARPT -- TWICE. NOTING OUR DISTANCE FROM THE VOR AND OUR POS TO BE A DOGLEG TO FINAL (RWY 27 IN FLL); WE CALLED THE ARPT VISUALLY. WE WERE TOLD CLRED FOR VISUAL AND SWITCH TO TWR FREQ. THE ARPT WE SAW WAS DIRECTLY W OF OUR POS; SO A TURN TO THE W WAS INITIATED; THE ILS FREQ TUNED; AND TWR FREQ SELECTED. NO DME FROM THE LOC WAS INDICATING; HOWEVER; WE DID RECEIVE A FALSE LOC INDICATION SHOWING US S OF THE RWY CTRLINE. ABOUT A 10 MI FINAL FROM RWY; THE FO INDICATED THAT WE WERE INDEED LOOKING AT THE WRONG ARPT; AND I; TOO; AGREED. SIMULTANEOUSLY; THE FLL TWR CALLED SAYING 'TURN TO A HDG OF 180 DEGS IF YOU'RE LNDG AT FLL INTL.' A TURN WAS MADE; AND THE ARPT WAS VISIBLE ABOUT 10 MI AWAY. THERE WERE NO TFC CONFLICTS AND WE LANDED AT FLL ARPT UNEVENTFULLY. TOTAL TIME DURATION FROM ACCEPTING VISUAL FROM APCH CTLR UNTIL CONTACT WITH FLL TWR WAS LESS THAN 30 SECONDS. CONTRIBUTING FACTORS TO ACCEPTING A VISUAL UNKNOWINGLY TO WRONG ARPT ARE: 1) 3 ARPTS IN VERY CLOSE PROX TO FLL WITH E/W RWYS;. 2) HURRIEDLY ACCEPTING A VISUAL APCH; AFTER BEING PROMPTED TWICE IF WE HAD A VISUAL; 3) NOT HAVING RADIOS TUNED AND IDENTED PRIOR TO ACCEPTING A VISUAL FOR CONFIRMATION TO CORRECT ARPT; AND 4) FATIGUE.