Cities can be reasonably approximated as points, and it is therefore possible to put columns for latitude and longitude in the Excel file and then import them into ArcMap. To find those coordinates, there are a wide array of websites; some have well-known cities in a table [example], others let you look up the city [example], and a quick Google search will turn up many alternatives.
Esri has a walkthrough of importing XY data which should enable you to get the points into a map after you've entered it into Excel.
Provinces (or countries, etc.) wouldn't really look right as points, however. For those you should first find polygons for the administrative boundaries you're interested in. (I'd actually suggest looking through data from ArcGIS Online first, since it has many commonly used boundaries and may meet your needs.)
Then you can Join the Excel data for those provinces to connect the non-spatial attributes to the polygons. This will require a common field shared by both the polygons and the Excel file -- a numerical code, or a name, something that indicates how the program will know which rows match which data. (Note that this approach can also work for your cities/points, if you're able to find a dataset of points that covers all the cities you need!)