Many of the exhibits in the museums of the Arts District have stories behind them... and sometimes those stories are ongoing. The PCs could certainly be asked to help acquire a particular item for a museum, but for an adventure set entirely within the Arts District, they may instead perhaps have to deal with a museum exhibit that bears a previously unrecognized curse, or that attracts unwanted attention...
Example: Lately strange things have been going on at night in the Museum of Orelani History—exhibits have been moved around; curtains and cordons have been torn or knotted; furniture has been upturned. The owners suspect vandals, but the real culprit is an ancient suit of armor on display that is haunted by the ghost of an ancient warrior. The ghost's motive is not mere mischief; it is more powerful at night, and hopes to lure someone into the hall at night to investigate so that it can possess their body and leave its current location...
For the most part, the festivals of the Arts District are innocent affairs that at worst might encourage some debauchery. Sometimes, though, unsavory elements might use the noise and chaos of the festivities as a cover for more harmful activities like drugrunning or even human trafficking or the placement of nefarious enchantments.
Example: At the Festival of Song this week, a weird new nonsense song has caught on and is frequently repeated. When people start disappearing, it turns out that the words of the song are actually part of a spell devised by a group of wizards who made a deal with a powerful otherplanar being; the spell, repeated enough, will open portals and draw people through to their master's home to serve them. Of course, the people singing have no knowledge of this; the wizards responsible for the spell managed to get it to catch on as an apparently innocent ditty...
Artists can be temperamental, and the art world has its share of jealousy and oneupsmanship. A vengeful artist might decide to take out their frustrations on a cavilling critic, or on a rival artist. The PCs could be called upon to save the threatened individuals, or shadier PCs may be called upon to deliver the artists' vengeance themselves.
Example:Lamon Derlis, the lead actor in the about-to-open playThe Goldsmith's Apprentice, has gone missing. If he isn't found, his understudy, Charel Trague, is ready to take on the rôle, but the play's producers would really rather have Derlis back. In fact, Trague has been kidnapped and is being held in an abandoned theatre at the edge of the district—and the whole thing was arranged by Trague so he could get the lead rôle he thinks he deserved.
The Arts District is relatively safe from street crime, but some of the valuable exhibits in the museums and the celebrity performers attract a different and often more sophisticated class of crime than is common elsewhere in Lüm. Art thieves may break into galleries; forgers may pass off phony masterworks; kidnappers may abduct famous actors and hold them for ransom. Depending on the PCs' proclivities and morals, they could get involved on either side of such a case.
Example: The curators of the Museum of Ancient Art discover that a famous statue, Panathe's Dancer, has been replaced by a modern fake. The PCs may be able to find the real statue and identify the thieves, but they have an unusual motive—they learned that the statue was actually an ænified person under a powerful curse, and they want to restore him to life. Can the PCs retrieve the statue and return it to the museum—or is the right thing to do to help the thieves reverse the curse and turn the statue back into a living man?