Things from the city jail management (transferring to state or federal when appropriate - or to the hospital and back - or to the court and back, etc...), payroll (and staffing management), data mining, managing assments of property, scheduling housing or business inspectors, budget forecasting based on weather models, keeping track of all the permits and where they are in the process...
There is lots of places where information technology has a role. Not necessarily high tech, but rather managing the information that is flowing through the system to make sure that the proper data goes to the proper places.
Its not going to be glamorous, but it sure beats paper and excel spreadsheets in email.
While big consulting shops may be brought in from time to time to do a project - the role of integration that software with the existing systems often falls to a FTE employed by the city, state, or whatever. Keeping that institutional knowledge about how things work is often priceless (well, you can put a price on it - how long does it take to figure out the system that Stan left behind... and if that's a consultant doing that, how much are they billing you for that discovery work?). In many public sector shops, the preserved institutional knowledge that a team may have can easily run into the collective century or more. That is a lot of understanding of how things work that can't be effectively outsourced.
But cities of a sufficient size (pulling up Chicago because its probably larger than the sufficient size), you find https://webapps1.cityofchicago.org/traffic/about.jsp
> Chicago has about 2900 traffic signals throughout the city. About 470 of these signals are interconnected through a fiber-network that facilitates the centralized monitoring and control of signal operations. Whether interconnected or not-interconnected, the signals are programmed to synchronize with signals immediately around it so that vehicles will pass through the intersections most efficiently. New signals are added and old signals are modernized every year depending on the need and availability of funds. While OEMC/Traffic Management Authority is responsible for maintaining the signal coordination and timing, Division of Electricity at CDOT is responsible for the maintenance of the signals and CDOT is responsible for the physical design, construction, and timing of signals.
It appears that the City of Chicago maintains their own. As noted there, that is maintained by the division of electricity ( https://www.cityofchicago.org/city/en/depts/cdot/provdrs/tra... ), which also maintains all street lights and signs. When one gets to a point where the municipality knows that there will always be work for some number of people - its cheaper to hire those people permanently than contract it out. This also provides a better SLA for the city (tax payers get rather annoyed if the street light is out and the response from City Hall is "we told the contractor about it, but they haven't responded yet - its the holidays.")