I have looked on the city and county website and can't seem to find it.
Not all cities have this data. There is generally a fee associated with acquiring it. It is generally beyond the resources of most cities to develop this data themselves. If a city does possess this data it is usually acquired through the County/Parish or Metropolitan Planning Organization/Council of Governments that the city belongs to. You may want to check at these places as well for this data.
As comments have suggested, if any of the above organizations do have this data, sometimes they do not make it public for download. This is especially relevant to more "expensive" datasets such as building footprints, LiDAR and aerials. You should contact the GIS manager at the above organizations to see if this is the case and, if so, if they can provide it to you. They are generally accommodating if you are polite and straightforward with your request.
It looks like some building footprints have been added in OpenStreetMap, but it is not complete. You can download what building footprints there are currently using Overpass-Turbo, I already made a query to search for all types of buildings you will just need to run it and then download the GeoJSON and work with it from there. If you need a shapefile you can use QGIS to convert the GeoJSON.