This is a simple one that will keep your players busy for some time as they attempt to restore their good names. With new group that has not made a name for themselves yet it can be as simple as a thief in the market drops a precious gem or magic item in one of the players pockets and to throw off the city guard he declares that the hero made him do it !
If the party is a bit higher level and has been drawing the attention to themselves by thwarting a powerful NPC’s plans. Mix it up by having the crime committed by the players themselves. This can be done in many ways.

Maybe he uses a front man to higher the PC’s to steal or destroy something for him. Killing two birds with one stone. The players now have unwittingly assisted their Nemesis and now have to answer to the powers that be for their actions or even risk imprisonment or becoming hunted themselves. If the later frame job would not work because the players would not take the job. Higher an illusionist to do the job while wearing the faces of the players. Now the players will have to have a very solid alibi to wiggle out of this trap. If all else fails send in the ever fun always enjoyable Doppelganger. They are always a bit of good old school fun! And last but not least the pay off; leaving the players to have to follow the money trail to whom ever set them up.

I hope you enjoy this Hook of the day. Go forth and catch some players in an enjoyable side quest plot.