Categorizing Content / Creating a Directory

Does anyone know if it's possible to create categories for content that isn't a blog post or product?

I need to build a directory of businesses. For example, I'd like to have a page of bars and restaurants with a secondary navigation (or categories) for 'breweries', 'casual', 'fine dining', etc. for users to narrow done within the directory on the same page.

This is close to what I am hoping to build: https://www.helloburlingtonvt.com/things-to-do/attractions/ 

Creating that type of experience is going to be a big project. Using a blog would work as it natively gives you access to categories and tags. You will very likely want to explore using this powerful filter plugin:

https://www.squarewebsites.org/squarespace-plugins/universal-filter

It will work for other pages, e.g. Portfolio pages, but with more limited categories (but portfolio sub-pages have much better design options than blogs, and don't have constraints with dates)

Looks like a good project, good luck, and if you need more help or suggestions, please follow up!

The link you posted is for a Simpleview CMS site. CMS is a content management service. The CMS is built just to do what you want. 

Your best option with Squarespace is to create a blog page in the unlinked section with each business having its own post and assign a category for the type of restaurant it is.  You create a page in the linked section of your site (or use a second blog which I will explain why ) with images and text for your main gateway to the subcategory of the type of restaurant.  You put a summary block on that page one (or more if you need more than 30 posts per block)  for the category with a text title like restaurants You can adjust the layout of each "business" block. You can string the blocks together on the same page (each block holds 30 posts)  and put a sidebar "directory" which is a modified archive block using the same categories. The category should be the name of the business. You can create drop-down menus on the Nav bar with links directly to the sub-category summary block and from there reach the individual restaurant or business.

I am doing something like this now, only I am using two blog pages, one for each individual post and one for the categories those posts are in. The second blog is my main category and it is in the linked section of my site, the blog with the actual posts, in your case each restaurant or business, And I have links on my nav bar and a directory of categories that can be breweries or causal or whatever you want. It takes time to do this but I built it from scratch using no plugins. I used code to hide the date published and to change the look of the summary block items.  I have a comments field but that can be turned off in order to make it not look like a blog page. You can also hide the category assigned to each post. Take a look and see if what I have done can be modified to meet your need. Check out the blog and the Nav bar. 

my random views

Thank you both for your advice! These solutions are much appreciated!!