A large percentage of most cities' taxes pay for the public school system. Because most of the children in any city are students in the public schools from the age of around 5 until 18, many teachers and support staff are needed, and many buildings are required to house all of these people. Taxes pay for all of this, although some of those taxes may come from the state or federal government.
The infrastructure of a city is primarily paid for with city tax dollars. Infrastructure includes the road system, electricity, gas and water lines, sewers, public parks, libraries and any buildings or other properties that are owned by the city. Cities often gain income by renting out city-owned properties that aren't being used by the city, but these amounts are generally quite small in comparison to the portion of the budget that comes from taxes.
Police and Fire
Police protection and firefighters are two of the more conspicuous of the many municipal departments that are paid for with tax dollars. Although people often grumble when the time of year to pay their taxes arrives, most people don't have a problem with the fire department showing up if their house is on fire, or with a police officer coming by to take their report if their house has been burglarized. Police and fire are supported by the city because a majority of the public recognizes that it is in everyone's best interest to have fire and crime controlled in a fair and publicly funded manner.
Town offices and the bureaucrats who run a town are all supported by public tax dollars. This situation sometimes causes public outcry in cities where property taxes go up and it is then discovered that the very administrators who raised the taxes are making huge salaries. Striking a balance between paying high enough salaries to attract competent people, and low enough salaries to placate the public, is one of the many balancing acts that are necessary when dealing with municipal finances.
City and State Taxes
Some of your city taxes may go to the state in which your city is located, as a part of funding transfers that occur between municipalities and state governments. Conversely, some of your state income taxes may end up coming back to your city, for example, as matching funds in the event of state-supported infrastructure development. This often happens when a city is building roads or highways in its territory.