Here are two things the Rusty Ruins mean to us:
(1) To Tally, the Rusty bridge that she uses to break in to New Pretty Town is a reminder of how solid the Rusty civilization was in comparison to the new society built on hovery technology. Unlike the new hover technology, this bridge is really solid: "It had been built so long ago that it held up its own weight, without any support from hoverstruts. A million years from now, when the rest of the city had crumbled, the bridge would probably remain like a fossilized bone" (1.15).
In comparison, New Pretty Town is built on hovery technology. And if that tech fails, then the whole city will collapse: "If all the pretty toys somehow stopped working, just about everything in New Pretty Town would come tumbling down" (2.4). Rusty Ruins are a symbol of a civilization built to last—compared to the hovery society that she lives in.
(2) To David and Tally, the Rusty Ruins are a symbol of how easy it is for a civilization to fail. The Rusty civilization relied so much on oil that, when oil became infected, Rusty cities fell into ruin. David's lesson? "Every civilization has its weakness. There's always one thing we depend on. And if someone takes it away, all that's left is some story in a history class" (40.60). Even if the Rusty bridge survives, most of the civilization passes away pretty easily. (And by "pass away," we mean caught on fire.)
So the Rusty Ruins are a little confusing: both a symbol of how easy it is for a civilization to pass away and a symbol of how something might survive. Maybe the Rusty Ruins are a hopeful symbol that the pretty system will fail, but some good part may be kept. (Like, let's get rid of brain lesions and keep the super healthy teeth, so we never have to go to the dentist again.)