Before you get to relating things in WordPress, you should decide what things are.
In a very nutshell there are:
- Posts of post types (native ones being pages and blog posts)
- Terms of taxonomies (native ones being tags and categories)
There are some things that WordPress does smoothly out of the box. Such as post being assigned a term or term having a parent term.
Others are completely missing, notably post being directly related to another post.
From your description my educated guess would be:
- Gallery post type
- Artist taxonomy
- Place taxonomy
But depending on specifics of data involved there might be nuances to push it in different direction entirely. While defining taxonomies and custom post types is quite easy in WordPress, effectively making use of them takes a bit of practice.