I've found two ways of doing this. The first is to set up a library with the categories in a drop-down menu, and have the first category of links be a dummy category like, "Select a location," that has no actual links in it. On the settings for that library, you would choose, "Only show one category at a time," and choose your dummy category as the "Default category to be shown when only showing one at a time." You would choose Ajax as the switching method.
You would then create a page that has the following code in it:
where X is the number of the library you just created. This creates a page with a drop-down menu in which, after someone has chosen a category (location) and pressed the "Go" button, the appropriate links are shown. The only problem with this method is that before someone chooses a category, the page will say "No links found" after the drop-down menu.
The only other way I have found to make this work is to manually create separate pages. You would create a main page for the categories. You would then create subpages of the main page, each of which would have the same slug as the slug for the category (location) involved. For example, if your categories had the slugs location1, location2, etc., your main page might be links, and your subpages would be links/location1, links/location2, etc. Each of the subpages would have this line of code:
[link-library categorylistoverride="X" settings=Y]
where X is the category (location) you want to display on that page, and Y is the overall library with all the links.
The main page that would have only:
In the Library settings page for Library Y, you would specify HTML Get + Permalinks as the switching method, check the "Enable Permalinks" box, and specify the main page as the permalinks page. That way, the main page would display the list of categories, and would link to all of the subpages.