I know nothing about the history of my city. I curious how it got its name, who settled it, or any major events that has taken place.
Try state, county, and city historical societies. Also museums.
Your local library would be my first stop. Most libraries have a local history section, and the reference librarian would be more than happy to show you where it is.
I did that one bitterly cold winter day. I went to the Public Library, bought a coffee and curled up in a comfy chair with all the books about my city that I could find there.
I recommend the library first, or the planning department at City Hall, or finding an old person sitting alone at a coffee shop or on a park bench and striking up a conversation.
Could also try googling your city to see what turns up, e.g. Edmonton.
Wikipedia has pretty good writeups for a wide range of cities. Some include detailed history - examples include Longridge, England, or New Brighton, MN. Check out your city there and see what you get. Barring that, visit your local library and ask the librarian.
How big is your city, how old is it, how curious are you, and how much free time do you have on your hands?
It might help if the OP just told us what her city is.
The Internet, obviously. Wikipedia is a good start.
Many cities have tourist centers as well with helpful pamphlets and folks working there who are very passionate and knowledgeable about the town.
City and state please.
Both the local library and tourist office are good places. Some public libraries even have departments for local stuff. I have done family research at a public library near where some of my ancestors homesteaded - they had CRAPLOADS of stuff on my family, including actual original physical documents related to their property.
There may be more than one level of tourist office - if you are in the US, check the State, County, and City to see if they have a tourist office presence. This may depend on jurisdiction - some may have tourist offices run by the State, elsewhere they may be run by the County. In Virginia, there are tourist offices at highway rest areas that are presumably run by the State, and I know that at least Prince William County has its own office that is labelled as a tourist office of Prince William County, though they have materials for tourism beyond and it may just be a sign thing - the funding may be the same.
If you are American and looking for some really in-depth stuff, try Google Books. A lot of self satisfied rich guys in the 1800’s wrote histories of their towns (and by implication ancestors) back then. Here is one for my hometown. They can be pretty interesting because these guys were a lot closer to the source material than we are. A lot of time that have info on all sorts of stuff that has been totally wiped out by modern development.
Edit: And here is one from the city my dad is from.