There's a lot you could do related to cost savings and efficiency. You could show how you can use GIS to route trash services or drainage complaint responses more efficiently allowing smaller crews and faster response time. GIS is also often used in cost-benefit ratio analysis for things like floodplain buyouts or environmental mitigation (these can help a city get money through federal grants). Self-service web maps also save money by reducing the number of call takers you need (citizens can log on using their mobile device to see if an electrical outage was already reported).
Unrelated to making money or saving money, GIS can help map where your city revenues are coming from and where they are getting spent. A lot of cities have issues with perceived inequity (the rich part of town gets all the new parks kind of thing) and GIS can show whether this is true or false. You can use pie graphs or other cartographic methods to show the breakdown of spending by department by geographic area (maybe your downtown is getting a lot more spent on roads than your suburbs due to aging infrastructure). You can also use GIS to help predict where you will need to spend money in the future (most concrete pipes last 50 years so you can map the length of pipes near subdivisions greater than 50 years old to estimate how big of a budget your drainage utility will need).
Some population growth models are also GIS based (and growth equals expanded tax base which must be balanced with expanded city services). GIS is also great for city planning to help make your city a desirable place to live (keep people out of floodplains, give them sustainable transport options, everyone close to greenspace, preserve scenic views) so you don't lose tax base through people leaving (think Detroit).
Just a few ideas to get you thinking!
