How can I adjust the height of the Google map on the contact page. I tried applying custom CSS of:

#map_canvas (
height: 360px;
}

but that broke the whole site.

There is no option in the settings. How can I do this please?

Edit your contact.php, in it you will see the div itself that holds the map:

<div id="map_canvas" style="width:100%; height: 460px;"></div>

Change its height to whatever you want. I don’t see how adding that CSS you did would break the site… maybe something else happened in the background…