Age of Z sounds like an interesting game. There's a lot of good zombie games.
There are a bunch, this one is more focused on the city building though so that makes it fun.
City builders are fun. How does it compare to games like SimCity?
A little less like Sim City then others this is more around building a city to compete in events with your team mates.  
Well it's got zombies, that's pretty different. Do they attack your city and you and your teammates can fight them?
Yes in some events, other events you and your team attack other teams. Sometimes you find things on the map tons of different interesting events.
It sounds kind of like Clash of Clans where you make a base and then compete with other players' bases.
Yes exactly like that but I don't think clash of clans has teams but I have never played so I don't know
It sounds fun to build, defend, and survive in a game like that.
It is great fun and if you have a good team it can be social as well which can be helpful when you are bored.