I thought a week without additions is probably enough to start new categories so here they come.

Phoenicians (5)
http://www.worldheritagesite.org/categories/category65.html

Kerkouane
Sabratha
Carthage
Tipasa
Tyre

Have visited all but the first. The main problem with these is that all, again except the first, in terms of the majority of what remains, are primarily "Roman" and get in to this category (should they???) because of who founded them
I don't see that any of them are significant enough, even as Roman towns, to get in our list - despite having their interests. That domain has lots of competition!
Carthage is possibly a " Maybe" largely because of its historic resonance.
The only "Punic" site, as per Wiki, wasnt occupied by the Romans and its remains date to 4th/3rd C BC- again from Wiki these do not seem significant enough to get it included

As you say Kerkouane is solely Punic so you can see all parts of the planning aswell as the well preserve aspects of everyday life. It is a very pleasant site to visit and provides an archeological insight into a significant civilisation, well worth a trip of you are ever in Tunisia. That being said I'm not sure it would get into my top 200 when I get around to voting, so probably a maybe from me.

Carthage would be the most obvious other choice but as pointed out the scant bits that do remain are Roman and not hugely significant. However the remains of the ports are very much in evidence as is the tophet supposed site of child sacrifice, I think I would stretch to a maybe on Carthage as well, though again I'm not going to argue too strongly for it.

Carthage definitely has huge importance in history of human kind. I vote for it (yes from my side, though most of it are Roman).
No to all others

Carthage (although close to a maybe for top 200)

Summary:

Kerkouane
Sabratha
Carthage for its historical significance
Tipasa
Tyre

Bringing these over to the main summary page at http://www.worldheritagesite.org/allbyrank.php