Is there any data-point on the Merchant Object that describes what type of merchant it is. For example; restaurant, hardware store, gym, cafe, bar etc.?
No, there isn’t any data on the merchant object that would identify what type of business they are. That information is in the Locations API mcc which is the merchant category code. You can use that code to identify what type of business the location is. 
Thanks @Bryan-Square. I’m wondering how many Square merchants have different codes for different locations, or whether they generally tend to use the same code for every location. I’m leaning towards the latter as most businesses only do one type of business, but I guess the scope allows for both options right?
I’m looking to automate the setting of an mcc from the merchant’s locations via the API, but don’t know whether it is worth it on the off chance they have different codes at different locations, and whether it might be better to get them to manually put in their business type.
I’ve seen quite a few sellers that have a different mcc for multiple location. So it does happen. However the vast majority of sellers use the same mcc for each location.