There are a total of ten plague hearts around the map. Some will be part of missions. Most of them will be on your own.
You can find them by using the command center, or spot them with billboards, but frankly as you drive around, you'll find them rather easily near where lots of plague zombies roam.
There is a rather straightforward method to destroying them, which surprised me because I dreaded them at first.
First, have a follower. Second, thin out as many zombies, hordes, and freaks near the heart as you can. This can be by sneaking around the building, or by brute force with your truck. Regardless, kill as many zeds as possible before you attack the heart.
You'll need your normal meds and stamina, but the key is molotovs and soda bombs. Bring at least 9 molotovs with you.
When you go into the building, you shouldn't see any other zombies. If you do, take them out. Then line yourself up and spam ALL your molotovs st the heart at once. Follow it up with the soda bombs, and then unload your gun into it. The molotovs do an incredible amount of damage to a heart.
Since killing a heart kills all the plague zombies, the building will likely be clear for you to search. By the time I got toward my last few hearts, I wasn't even using any meds or stamina since they went down so quickly.
Hope this helps!