Why would the city be liable for shitty robot behavior?

Maybe you could construct a situation where they would be but I can't imagine it would be one that would play out in real life. A city allowing robots to operate would make the robot company to follow all applicable laws" including ADA so unless the city's lawyer is really really bad this lands on the robot company.

Whatever entities, city or state which are doing the licensing and permitting I'd imagine might be able to be sued.

Because it's a bit of a unique new situation with no caselaw, it would be a pretty open question of who could be sued for what.