The issue with Uldah is kind of a circular self-sustaining problem.
People stay in Uldah for a number of reasons. I am not a big group player (I play in teams of 2-4 statics), but I stay in Uldah regardless because of the following
1) Uldah's map layout is the most efficient. The Market Ward is right next to the Aethyrite, the shops are relatively nearby, and the Adventurer's Guild is easily accessible.
2) The city offers a lot of repeatable in-city crafting leves. Having to travel all the way to camps just to turn in leves is a huge design flaw for me as a lazy player who hates having to run across tracts of empty land just to complete these crafting leves.
3) The city is in between LL and Gridania - now that we have airships this isn't as much of an issue, but I think this was one of the original reasons why I stayed in Uldah.
4) This one's the most important - a lot of people stay in Uldah because a lot of people are there. Because a lot of people are there, a lot of people stay in Uldah. A lot of players stayed in Uldah for reasons 1 and 2. Before airships and chocobos were introduced, a lot of people stayed in Uldah for reason #3 so that they can get to Grid or LL in an ok amount of time. This was back when we had an extremely flawed anima usage/teleport system.
5) Lots of people = easier to get pickup groups and the shout radius is very large.
6) Lack of Global Chat/LFG channel that is featured in most modern MMOs. This one's probably the big kicker. I'm sure if Yoshida & co. could implement such a channel with the slapdash mess that is the FFXIV 1.x code, they would've done so, but since they can't, people have to adjust and simply spam shouts in the most populated area, which is Uldah Zone A.
7) Slow walkspeed in town without Monk = stay in the town that makes you walk the least, which is Uldah.
Basically, Uldah is one giant huge design flaw that we can't do much about; its attractiveness for practicality is further worsened by the sprawled out and inconvenient designs of the other two cities, which are design flaws upon themselves. The devs have done the best they can to try to patch around these flaws and add features to encourage people to move out of Uldah (increased anima regeneration, lower anima costs for teleporting, airships, chocobos, favorited destinations, universal auction houses, etc), but I think this is a case of too little too late. The game would have to be redesigned from the ground up so that the three cities are equidistant from each other and so that they either offer similar services so that there is no preference for ALL players to stick to one city or completely UNIQUE services that give players a strong reason to stick to one (different) city versus the others.
tl;dr: Wait for 2.0.