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This one would be in a freemarker template file at widget/featured-places-widget.ftl.
You could overlay that in the theme if you were so inclined but may need to alter the css accordingly.
One thing to note, if you're looking to bring the whole site up to best practices like proper use of <h> tags etc. you're going to have your work cut out for you. There are a large number of templates (>500 freemarker and >600 soy) and probably a lot of them (such as widgets) are legacy. If/when you upgrade, you'll most likely have to do it all over again. I guess I'm saying, pick your battles.
Hope this helps,