B737-300 CREW DECLARED A LOW FUEL EMER AFTER LONG HOLDING; LINEAR ATC DELAYS AND POOR ATC HANDLING; WHILE ATTEMPTING TO GET INTO STL.

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FUEL ESTIMATE. WE DEPARTED ZZZ AFTER A GND HOLD OF 1 HR 30 MINS FOR ZZZ3. ONCE ENRTE WE WERE INFORMED OF POSSIBLE HOLDING FOR ZZZ3. CALLED DISPATCH OVER ZZZ RADIO AND INFORMED THEM OF POSSIBLE HOLD INTO ZZZ3. SAID WE WOULD CONTACT THEM OVER ZZZ3 RADIO IF HOLDING WAS GIVEN. WAS GIVEN HOLDING INBOUND TO ZZZ3 AT TRAKE INTXN. CALLED DISPATCH TO GIVE INFO ON TRAKE HOLDING. WITH ALL OTHER ACFT HOLDING IN AREA AND ACFT IN VICINITY OF ZZZ3; IT WAS VERY DIFFICULT TO COMMUNICATE CLRLY WITH DISPATCH. AMENDED OUR ZZZ1 ALTERNATE TO DUAL ZZZ2 ALTERNATE TO INCREASE OUR TIME TO STAY IN HOLD AT TRAKE. AFTER LONG HOLD AND SEVERAL INCREASES IN OUR EXPECT CLRNC TIME WE LEFT HOLD AT TRAKE FOR RWY 30R ILS ARR. ATC CONFIGURED US ABEAM THE ARPT DUE TO SPD LIMIT OF 180 KTS THEN ATC FLEW US ON A 30 MI DOWNWIND BEFORE TURNING US BACK TO THE ARPT. WE WERE ON A 2 MI FINAL TO RWY 30R WHEN ATC INFORMED US OF A CONFLICT WITH ARRIVING TFC ON RWY 24 AND TOLD US TO GO AROUND. WE MISSED THE APCH AND ASKED FOR CLRNC TO ZZZ2. ONCE LEVEL AT FL220; I RE-ENTERED OUR ZZZ2 DEST IN FMC ONLY TO HAVE THE FMC TELL ME WE WOULD LAND WITH 2.2 OF FUEL LEFT. WE HAD LEFT THE HOLD WITH 10000 LBS OF FUEL ON ACFT AND MISSED APCH WITH 7000 LBS. I WAS NOW LOOKING AT 6500 LBS REMAINING ON THE FUEL GAUGES AND COULD NOT FIGURE OUT WHY WE WOULD ARRIVE ZZZ2 WITH ONLY 2.2 REMAINING. HAD FO DECLARE EMER FUEL TO ATC AND DIRECT A CLRNC TO ZZZ2. ONCE WE WERE GOING DIRECT I GOT BACK INTO THE FMC AND DISCOVERED THAT ZZZ3 WAS STILL IN THE FMC AS OUR FINAL DEST AND THAT'S WHY WE WERE GETTING THE LOW FUEL NUMBERS. FOR OUR ARR FUEL; I CORRECTED THE FMC AND IT THEN SHOWED US ARRIVING ZZZ2 WITH 4200 LBS OF FUEL. WE CONTINUED TO ZZZ2 AFTER UNDECLARING EMER FUEL WITH ATC AND LANDED WITH 4000 LBS OF FUEL ON THE ACFT. CONTACTED DISPATCH TO DISCUSS WHAT HAD TAKEN PLACE. SUPPLEMENTAL INFO FROM ACN 536898: DEPARTED ZZZ AFTER 90 MINS GND STOP TO ZZZ3. IMMEDIATELY AFTER TKOF; ZZZ3 GND STOPPED AGAIN. HELD FOR ABOUT 90 MINS. WE CALCULATED 3300 LBS TO DIVERT FROM MISSED APCH. (DIVERT TO ZZZ2) ALSO ADDED 5000 LBS FOR LNDG AND 1000 LBS FOR APCH. WE ACCEPTED VECTORS FOR APCH WITH 9800 LBS REMAINING. WE WERE DIRECTED TO SLOW BELOW 200 KTS WITHIN 10 NM OF THE FIELD ON DOWNWIND. THEN WE WERE VECTORED TO A 30+ NM FINAL. ON ABOUT 2 NM FINAL (LESS THAN 1000 FT AGL) WE WERE DIRECTED TO GO AROUND FOR XING TFC. (WE WERE ON RWY 30R; TFC ON RWY 24.) WE WERE ON THE SECOND ACFT SENT AROUND IN A 30-60 MIN TIMEFRAME. WE IMMEDIATELY STARTED OUR DIVERT TO ZZZ2. ATC COULD NOT CLB US OUT OF 6000 FT UNTIL 15+ NM FROM ZZZ3. FMC SHOWED ZZZ3 AS DEST AND RPTED ARR FUEL AT 2200 LBS. KNOWING WE WOULD HAVE LESS THAN 4000 LBS AT ZZZ2; WE DECLARED MINIMUM FUEL AND WORKED ON THE FMC. (WE HADN'T YET FIGURED OUT FMC DEST WAS STILL ZZZ3.) NOT SURE OF WHAT FMC WAS TELLING US WE DECLARED EMER FUEL. IMMEDIATELY AFTER DOING SO WE DISCOVERED OUR PROB AND CANCELED THE EMER. WE LANDED IN ZZZ3 WITH 3900 LBS.