Hi!
I'm not exactly sure what you mean by crazy links....
I think you are on the right track. First create a Search & List Type for the Categories with a single menu item pointing to City (in your case). That will list all of the cities.
Then build another Search & List Type for the Articles (museums). You can build a menu item for this, and then make a note of what the URL is because you can use that information to build your HTML link.
Back in the Category Search & List Type, on the City Name you can add a link on the Typography (option #2) using the HTML option.
If the museums in their own Content Type, then the url might be something like so:
<a href="/articles?cck=$cck->getValue('cat_title');">$cck->getValue('cat_title');</a>
It will depend on what your URL looks like for the second Search & List type. All you need to do is copy the parameters from the Category Search & List Type and build that into your HTML link.
Hope that helps.
Randy