I am going to show you the sink, kitchen and fridge

Solution 1:

As others have said in the comments, the nouns in your first example are not quite related in the right way to justify omitting the articles: instead of kitchen, you need to have an item that, like the sink and the fridge, is typically found in a kitchen.

I agree with you that the second example is marginally acceptable. It's only marginally acceptable because both campus and school need to be interpreted in a particular way for the sentence to work, and not in the way the overall context most naturally suggests. In the end, to make the sentence work, we interpret campus not in the sense in which the accommodation and school are part of it (that was the problem with kitchen in your first sentence), but rather as something like the grounds, i.e. what the open areas and the exteriors of the buildings look like. School is also a bit iffy; to make the sentence work, I think our mind tries to interpret it as a particular building.

Discussion

According to Collins COBUILD English Guides: Articles, articles can be left out

when two nouns (or adjectives), both acting as head of a noun group, are joined together with 'and' or 'or'; the second head can be without its article. This happens with both the definite and the indefinite article.

They had enhanced the reliability and quality of radio reception.
…a coffee cup and saucer.
You can order traveller's cheques through a local bank or travel agent.

You don't have to leave out the second article; you can say 'a coffee cup and a saucer'. But if you do leave it out, the two nouns must be closely related in meaning; you couldn't say 'There was a matchbox and jacket on the table'.