MikroTik

I want to create a network that only allows access to certain web sites for both HTTP and HTTPS traffic. I was able to get HTTP to work using NAT and Web Proxy, but am not sure how to work with the HTTPS side.

I also played with the Hotspot feature, and it somewhat works in that when it's on, I can add certain websites to the Walled Garden list, and be able to view only them (both HTTP and HTTPS) without entering the username/password. However, I don't want the login functionality of a hotspot. I simply want to block non-approved HTTP/HTTPS traffic. Any ideas on how to do that?

Hotspot is a good way to do this. Just make the hotspot splash page that says something like "The page you are trying to access is not accessible on this network".

By splash page, do you mean to replace the existing login page?

Yes