How do I include a page in a site but not have it show up on the main top left navigation.

If you want a URL you can call externally, you either have to add it as a site page or you'll need it to be a record view.

Alternatively, you can create your top level pages and have a secondary navigation which shows or hides things with dynamic links but the sub pages will not be accessible via a URL.

You can find examples of secondary navigation on Appian's design page: [View:https://docs.appian.com/suite/help/23.2/sail/secondary-navigation.html]

WIth a little workaround, you can also call pages from your side navigation menu using textCache plugin. What it does is, it will allow you to store a value as a temporary cache and then you can get that value on some other screen and based on that value, you can open a certain screen. Like 1 for screen A and 2 for screen A, etc. 

Interfaces do not have an URL. The only addressable UI objects in Appian are pages in site and record views. This does not include tasks and a few other things, not relevant in the context of this question.

I honestly can't quite tell whether this is the sort of thing you're after here, but i wanted to add my own advice to the list of other good suggestions above:

it's trivially easy to make an interface (i.e. a site page) which contains a list of "links" to other interfaces, wherein those links are actually just dynamic links saving a marker into a local variable (like a name or an ID number), and when one of them has been clicked, hide the entire original interface and show the desired child interface instead (with the potential to easily add a "close" button/icon, breadcrumb trail, etc, at the top of the screen allowing the user to click back to the initial list of links).  We do this all over the place in our system to allow navigation without having zillions of things at the top of the site (and also that's the reason they only allow 5ish top-level Site tabs, too).