How can I create new layouts for the filter page.

I'd like to be able to dress it up similar to this page:
https://ncsciencefestival.org/find-events

Where/now can I do this?

It will require much customization in this case, you can check out this guide for how to override layout in JA Megafilter: https://www.joomlart.com/documentation/joomla-component/ja-megafilter#override-layout

If you're not familiar with code, I recommend you to hire a developer to get it done for you.

Regards