A B757'S DEST DEVELOPED CAT II/III WX BUT HAD INOP RVR. THE FLT PROCEEDED TO TWO ALTERNATES WITH BELOW MIN WX BEFORE LNDG AT AN UNSCHEDULED ALTERNATE WITH 6.5# FUEL.

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ARRIVED AT ZZZ1 WITH WX AT CAT 2/3 MINIMUMS. ZZZ1 TWR STATED THAT EQUIP DID NOT WORK FOR THE CAT 2/3. WE HELD FOR ABOUT 1 HR UNTIL OUR BINGO FUEL OF 14.0 LBS. WE WERE ASSIGNED A NEW ALTERNATE; VIA ACARS; OF ZZZ2 IF WE HAD TO DIVERT. WE DEPARTED ZZZ1 AT OUR CALCULATED BINGO FUEL OF 14.0 LBS TO ZZZ2 TO LAND WITH APPROX 9.0 LBS OF FUEL. ENRTE TO ZZZ2 WE DID ANOTHER WX CHK AND SAW THAT THE WX WAS NOW AT 1/4 SM AND FOG (BELOW LNDG MINIMUMS). WE IMMEDIATELY CONTACTED ATC CTR AND ASKED FOR DIRECT ZZZ3 BECAUSE THE INITIAL WX REPORT REPORTED THAT WX AT ZZZ3 WAS ABOVE LNDG MINIMUMS. I THEN CONTACTED COMPANY AND THEY CONCURRED. ONCE AT ZZZ3 (FUEL NOW AROUND 9.0 LBS) WE NOTICED THAT THE WX WAS ALSO DROPPING. TWR STILL RPTED WX ABOVE LNDG MINIMUMS. WE CONTINUED WITH VECTORS FOR THE APCH. ACR Y WAS FIRST ON THE APCH; WE WERE #2 FOR THE FIELD. ACR Y COMMENCED THE APCH AND WENT MISSED APCH. WE THEN ASKED FOR AN IMMEDIATE CLB TO 10000 FT DIRECT TO ZZZ4 (FUEL NOW AROUND 8.0 LBS). WE CALCULATED FUEL REMAINING FLYING DIRECT TO ZZZ4 WAS 6.0 LBS; NOT INCLUDING THE APCH OR DSCNT. I HAD MY FO CONTACT ATC AND TOLD THEM WE WOULD BE MINIMUM FUEL AND WANTED DIRECT TO ZZZ4. ON SECOND RADIO I HEARD ACR Y GET VECTORS DIRECT TO ZZZ5 AND WAS ALSO IN A MINIMUM FUEL SITUATION. ZZZ5 WAS ONLY 40 NM AWAY COMPARED TO ZZZ4 THAT WAS 80 NM AWAY. CTR ALSO SUGGESTED ZZZ5 AIRFIELD AS A CLOSER ALTERNATE SINCE WE WERE STATING THAT WE WERE MINIMUM FUEL. AT THE SAME TIME WE WERE ALREADY SEARCHING FOR THE PLATES IN OUR BOOKS AND COULD NOT FIND THE FIELD INFO. I THEN ASKED CTR TO DIRECT US TO THE ZZZ5 FIX AND THE IDENTIFIER AND OTHER AIRFIELD INFO. ACR Y ALSO CHIMED IN WITH INFO ABOUT THE FIELD AS THEY USED IT AS ONE OF THE ALTERNATES AND HAD THE INFO READILY ON HAND. 10000 FT RWY; CLR WX; CALM WINDS. TO MAKE MATTERS WORSE ON DSCNT AND HDOF; ATC GAVE US VECTORS TO ZZZ6 INSTEAD OF ZZZ5. I NOTICED THE DISCREPANCY OF THE VECTORS NOT GOING NEAR THE NAVAID OF ZZZ5 SO I DECLARED AN EMER AND ASKED FOR DIRECT TO THE AIRFIELD; NOT KNOWING THAT THERE WERE 2 ZZZ5 FIELDS. IT WASN'T UNTIL I ACQUIRED ACR Y VISUALLY WAS I ABLE TO FIND THE FIELD WE WERE BEING VECTORED TO. FO MADE VISUAL APCH; AS WE LANDED UNEVENTFUL WITH APPROX 6.5 LBS OF FUEL. SUM: 1ST LNDG ALTERNATE DROPPED BELOW LNDG MINIMUMS. 2ND LNDG ARPT DROPPED BELOW MINIMUMS. FUEL AT TIME OF 2ND ALTERNATE GOING BELOW MINIMUMS WAS APPROX 8000 LBS.