Demo Places Issues

Try

#primary-nav ul .sub-menu a {line-height: 30px !important}

Thanks

Change 30px to 42px.
Don’t be afraid to experiment and review https://wpgeodirectory.com/docs/customizing-your-style/ for more CSS tweaks.

Thanks

If it works, it works …

However, when I try to add the Claim Listing button widget, Compare button widget, and the Get Directions button widget, I cannot get them to appear in the same areas as on https://wpgeo.directory/supreme-directory/places/united-states/california/san-francisco/chinatown/

You need to add the “Claimed” custom field and make sure it is active. I added it for Places.

You need to add the Compare block to GD > Settings > General tab > Pages sub-tab > GD Detail page > Edit.
I added it.

You need to use the Post map and select to add direction in the map widget. Done.

And is the neighborhood automatically shown based on address?

You need to enable neighborhoods at GD > Settings > Locations > Enable neighbourhoods? > YES

And, any way to fix the listing description from being pushed all the way down on the detail page?

Not sure what you mean, maybe change the settings of the Report Content plugin to show the report button below content instead of above content?

For the Compare Listings button, how do I place it in the same position as in the demo?

By moving the shortcode or block to below the images block or shortcode.

Also, I’m not seeing the neighborhood show for any of the places. In fact, all of them have Honolulu for some reason.

A neighborhood will only be added if you update the address of the listing.

How do you just show “Category” as a widget and not the tags with it?

Either remove the tags from the listing, or hide with CSS.

.geodir-tags {display: none;}

Review https://wpgeodirectory.com/docs/customizing-your-style/ for more CSS tweaks.

How do you get the horizontal rule and subheaders to appear between each widget?

Add CSS, for example

.sd .sidebar .widget {border-bottom: 1px solid #ccc;}

Review https://wpgeodirectory.com/docs/customizing-your-style/ for more CSS tweaks, you really need to have a go at this yourself.
Have a look at https://wpgeodirectory.com/support-policy/ and we will only give customization advice if at least you try yourself.