Filter by category so that only those locations are shown on a leaflet map?

This thread might be useful for you:

Basically, the two approaches I’ve seen people use on this forum involve either using FacetWP (requires some PHP tinkering) or creating links that have URL query parameters like mysite.com/?category=type1 and then using the Url tag’s query attribute to modify your L&L template based on the value of the parameter in the current URL.

I hope that’s helpful for you!