There was actually a chain of babysitting missions, because I created a few mission chains that as they progressed, would draw the PCs into deeper aspects of plots within the city. One mission chain was "Assistant Exterminators" in which the PC's helped a halfling clean various critters out of the sewer. As missions progressed, they'd stumble upon a black market smuggling operation that used the sewer tunnels as passageways, that would ultimately connect to a plot of the Mayor of one of the city sections being connected to orginized crime, and a Mindflayer who was trying to subvert the city.
I digress. other babysitting missions. One was to spend the night with an infant child who was a "Chosen One", a naturally powerful sorcerer 6 month old, who was the fulfillment of some prophecy or another. You know, those kids are a dime a dozen. The problem was in the baby's sleep, he'd run the risk of summoning creatures out of his dreams. I had a chart worked up with various Summon Monster creatures and applied the Psudonatural template to make a twisted nightmare. I had the PC's sit in the nursery, than I rolled a d6 to determine if anything appeared. the dice was in their favor, no monster popped, and they got to be paid for an uneventful night.
There was a third babysitting mission I'm forgetting now, but the 4th one was going to involve watching over the child of a Noble family, a family involved in the City parlament (The City was the captial for the surrounding country), the PC's would be watching the child and I'd do my darndest as a DM to see that the kid would be kidnapped, drawing the PC's into some of the political intrigue and eventually leading to an audience with the King. We never got that far into the campaign so that one went unused.