When you finally make it to Rupert the Gunsmith's flat you learn that his wife has gone looking for Insulin for one of the kids that they are looking after - and that the kid really needs it bad. You volunteer to head over to the drug store and see if you can find some Insulin for the kid.
When you get to the families apartment and go inside there are a few infested to clear and some loot - in the kitchen there is a note on the fridge - the note explains where the father was going - you deduce that he got the meds but never made it to pick up his daughter - the pizza place was his next stop.
You radio Rupert and then head to that address... And find the dather's body - and the Insulin - on the floor there. Good on ya!
Now to head back to Rupert with the medicine - he gives you this speech about you staying here and looking after the kids - but the actual side-quest ends when you finish the chat so you can just leave. And that wraps up this side-quest.