I actually don't think people would flock to the cities. This is because, while the cities may have hardened defenses, it will be the first target of the undead. The undead will follow the people to the cities and in short order, someone infected will get in. The same defenses that these cities relied on will instead trap them within, leading to slaughter and feast for the undead.
I think people will rather become much more nomadic, intent on staying one step ahead of the horde. When faced with much more powerful undead variants, these groups may band together temporarily to take it down, and then disperse.
Society would probably break down with all this happening, making relatively cheap things like food or water highly valuable. The few existing strongholds, impervious to infection either because of the sheer difficulty in reaching or xenophobia, might very well experience a temporary boon.
Take for example a mountain of dwarves. Even if they encounter undead in their tunnels, they could easily collapse them to ensure no threat. Add to this the harrowing mountain path one has to use to reach their home, and the undead will have lots of trouble reaching them. However. let's say the remnants of the nearby human kingdom travel to the dwarves seeking add. Now any lord will know that it would be foolish to take in so many, so he regretfully turns them aside. He grants them a mercy though, and offers them the choice to exchange their possessions for supplies. The meager refugee's except and not much longer than that are on their way westward, perhaps due to the incoming winter. While they are traveling, they spread word of the dwarve's kindness, and soon many small groups are traveling to the dwarven stronghold to barter for supplies. The dwarves, having the upper hand in the trades, profit.