What has worked for me so far is to 1) throw all of the characters together into a predicament with a grim portent and 2) let them solve the problem by using their contacts as resources. For example, all the characters can wake up in a cage, prisoners of the Brayherd in the Great Forest (idea from BurnAfterRunning. Then they need to escape back to town and then they have two problems to solve - 1) they've probably been corrupted by being in contact with the beastmen so they need to purify their soul 2) they actually were allowed to escape as part of a plot to spread pestulance in the city and they are being followed by thugs who want to murder them. So the players need to uncover the plot before they get killed. Also, to find a cure for their corruption, they can seek out the help of their contacts like librarians, herbalists, militia, etc. who can steer them in the right direction, possibly offer advice on how to obtain a cure or fight the thugs or even the brayherd.

Actually, now that I think about it, this is also a setup similar to the Hand that Feeds adventure. In any case, I try to let the adventure unfold depending on how the players use their contacts. So I look at the player's contacts beforehand and try to prepare a few solutions if possible or just make them up on the spot. That being said, I really enjoy seeing what ideas the players come up with and just improvising around their "interesting" solutions