Let’s steal an idea from Mithridates. Your party is from a single area or perhaps a single race, or at the least has some sort of affiliation with a kingdom. They are visiting an outlying province, neighbor or what you might call a frenemy nation.
Unbeknownst to the party, war is about to break out. The local ruler has decided to initiate formal hostilities by killing every single person from the party’s country/race/whatever just after sundown. You can begin that afternoon, giving the party a head start, or you can begin en medias res as they are running from the local goons/assassins/army. They have to find shelter, food and supplies on their own and fight their way back to friendly territory. They might even want to help some fellow refugees on the way.
Since my semester ended and winter break began, I’ve been listening to a lot of the excellent podcast The History of Rome, learning something I have always wanted to learn but not had the time to. This is where I first heard of Mithridates doing just this, killing every Roman or Roman-friendly foreigner in Pontus and getting his neighbors throughout Asia Minor to do it too (which sort of guaranteed he wasn’t in this alone).