See for example the old stone bridge of Mostar (Stari Most), which had to to be rebuilt after the war, and they could only do it by finding old turkish craftsmen who were still able to build such a bridge, without steel. Modern architects all failed.
So if you're going to talk to lay people about ancient structures, you're going to talk Rome, or maybe some cathedrals, because otherwise you're not talking about the mechanics of ancient structures, you're talking about appreciation of otherwise unknown architecture, and that's not the same thing.
Stari Most is also a well-known tourist destination. Its destruction occurred during a war the US was involved in and its destruction, rebuilding, and symbolism in the war were widely reported in US media. [3] Today, it's popular on mainstream sites like reddit. [4]
1. http://web.mit.edu/akpia/www/generalinformation.htm
2. http://agakhan.fas.harvard.edu/icb/icb.do
3. https://www.google.com/search?q=site:nytimes.com+%22mostar%2...
4. https://www.google.com/search?q=site:reddit.com+%22mostar%22...
Regarding the Stari Most reconstruction effort I can recommend an excellent documentary by Jasmila Žbanić "Builders diary", and there are numerous more TV movies about the technical challenges there.