In terms of links, do you need to build links to your GMB page, Yelp page, etc., or is linking building primarily targeted to the website itself?

People link to things that are awesome. At least they should. So links to directory pages don’t make a ton of sense in a “perfect world” and probably don’t represent a reason to rank a business higher than another business as most of these links would be built by the business owner and not earned.

Now that Google My Business pages have a social layer to them, it makes sense that they could get links, get mentioned, etc. From experience it can help you rank higher in map results, but it will make your actual Google My Business listing rank higher for your brand name. Same with Yelp, I think the main reason a Yelp listing should be linked to is as a way to say “check out our Yelp listing for reviews.”

The type of links that help your map listing rank higher are ones that point at your website.