A CRJ-200 Captain diverted when his destination airport fogged in. The Dispatcher was unhappy the crew did not go to a different alternate.

Narrative

Before departing; I checked the release; METAR; and TAF as I always do. TAF at our time of arrival was showing: FMXX2200 12004 KT P6SM BKN040 and an alternate was not required. We had about 1000 LBS extra fuel for tankering. On taxi out; ground informed us that northbound departures were stopped; and we burned approximately 300 LBS of that fuel waiting in line for takeoff. We eventually were re-routed around weather and took off for our destination. ATIS winds calm; visibility 10SM BKN040 BKN080 19/18 A2987. We planned on the visual approach; briefed that; and was cleared for that by approach once the runway was in sight. When checking in with Tower; I noted some ground fog. I thought to myself that we made it in at a good time; as soon the airport would fog over. On base turn; Tower informed us that the fog was rolling into the airport; obscuring the end of our runway; however he had the full length in sight from the Tower. Turning final; Tower reported RVR 4000 FT. We executed a missed approach and complied with the Tower assigned heading and altitude; and requested vectors for the ILS. We were handed off back to approach. Checking in with approach; we were told the RVR was now 2200 touchdown; 4000 rollout. We needed 4000 for the ILS w/ ALS INOP. At this point we had 3700 LBS fuel on board. ATC assigned us some headings to fly; and we climbed to 3000 FT. I started checking for alternates; and attempted contact with our Dispatcher but received no answer. I assumed we were too low for radio service. I then sent an ACARS message saying our destination was below minimums and we needed to divert. At this point we climbed to 10;000 FT and entered a hold over the OM as published. I called the Flight Attendant and informed her we would most likely be diverting but I did not know where yet. In the hold we flew 200 KTS to save fuel; min clean speed at 47000 LBS was 182 KTS. We still had no response from dispatch so we decided to head to another airport. I saw that three airports were all in the same direction; give or take. I knew at least two of them were stations we served with passenger handling. We then pulled up the weather on the ACARS. At this point we got a printout from the Dispatcher with a flight plan to ZZZ; showing landing with 2061 LBS with a burnoff of approximately 1500 LBS. We had about 3400 LBS at this point. I thought that was too close for comfort although ZZZ weather was VFR. I sent a message back asking about a different airport; which we saw the weather was 1 1/2 SM 500 OVC. The Dispatcher replied that no airplanes have landed there for 3 hours. Scratch that idea. At this point we were about 40 miles from ZZZ1; which was reporting winds calm 2 SM 300 OVC. We had approximately 2800 LBS fuel remaining; and I elected to divert to ZZZ1. On descent the Dispatcher sent another ACARS message suggesting ZZZ2. According to the FMS that was 104 NM away; and landing with 1700 LBS fuel. I did not answer this message as we were already on approach for ZZZ; using my Captain's authority. We flew the ILS; and landed without incident; approximately 2500 LBS fuel remaining. At this point I parked on the vacant air carrier ramp; completed all checklists; and contacted the Dispatcher. The Dispatcher was irate that I went to ZZZ against her wishes. I informed her that I did not think the options she presented me were viable; and she continued to berate me on the phone over my decision. She claimed that I should have gone to ZZZ2 because it was only an hour bus ride to our destination whereas ZZZ was three hours. I told her that I was more concerned about getting the plane safely on the ground in our low fuel state; and that I would not entertain any further discussion on that topic; however I would like a plan on what to do from here. I did not feel that the Dispatcher was much help. I would have headed to ZZZ2 if I would have been informed that was the best option while we were in the hold; however she took what seemed like a long time to respond to our ACARS message. At that point I knew I had to get the airplane on the ground absent any further information from dispatch. Matters that complicated this were the awkward 1-way communication of ACARS and the poor weather at almost every suitable diversion airport.