Jordan is well worth a visit to see Jerash, Petra, Wadi Rum and other sites. You can also eat hummus 3 meals a day, which is a definite bonus. I went a few years ago with my family and it felt a lot more friendly, relaxed and safe than you might expect, given its location.
Also noteworthy in Algeria: https://en.wikipedia.org/wiki/Timgad
(I think I read somewhere that Algeria has the most Roman ruins outside of Italy, although I could be mistaken)
It's not even noon and I've already thought about ancient Rome today!
Seriously, when I am in Italy, I think of ancient Rome most of the time. The country is just chock-full of Roman structures and you won't be walking for a long time before bumping into one.
When holidaying in Italy I had the luck to pick the day trip one day. Really glad I found Paestum (an ancient Greek city): it is every bit as captivating as Pompeii imo.
Went to Italy for the first time a few years ago and picked paestum randomly when we needed a break from Naples. Went back last year and will probably go again.
So is Ostia, Rome's ancient harbor.
I’m currently reading “Carthage must be destroyed”. If you want to look at the event from a not-solely Roman perspective I recommend this
Carthago delenda est! That's how us noob Latin language students learn the gerundive, with "delenda" being a verbal adjective, meaning "to be deleted (destroyed)". As a bonus it's also useful as a paradigm for remembering how the passive periphrastic conjugation works. It helps that it also implies violence and destruction, making it easier to remember.
I wonder how many other "Pompeii of ___" exist. I also know of the "Pompeii of Central America" (Joya de Cerén in El Salvador).