At the “!” you meet the Witch - who when you talk to her tells you that she can make you something that will help you to avoid being noticed by the infected. She tells you to go to the caves to collect Black Mushrooms in order to make a tincture that will give you some protection against the infected.
The destination is an underwater cave - simply follow the marker to get to it. At night.
So yeah this sounds like it is going to be really hard but actually as long as you use the night vision booster and you take care to not make noise you can get to this pretty easy. There may be some regular zombies for you to deal with - and the running ones - and once you actually reach the marker there are ten (10) of the shrooms to pick. Just ten.
After you pick them head back to the Safe Zone and rest until morning, then head for the marker to turn in the quest and collect your reward, which is some of her potion (and attitude).