The tourist lied, and was really going to Iteropolis. She was able to deduce that the first robot was telling the truth, and that her true destination was therefore to the left, on the road the robots had been traveling.
The key is the first robot's second statement ("If you asked me, I'd say Bitborough is to the right"). If the first robot is a truth-teller, this statement can be accepted at face value: Bitborough is to the right. If the first robot is a liar, however, the statement must be a lie; but what is the lie about in this case? A careful reading shows that it concerns how the robot would answer a direct question about the location of Bitborough. If the true location of Bitborough is to the right, a robot that lies would say "to the left." If the robot lies about what it would say, it will say "to the right." Thus the actual location of Bitborough must be to the right in any case.
Since Bitborough is to the right, and the second robot directly contradicts this, the second robot must be a liar. Therefore the second robot's first statement ("That one's a liar") is false, and the first robot is a truth-teller. Thus the first robot's first statement ("We've just come from Iteropolis") must be true.