I'm slacking at work, and this seems like a fun way to pass the time. Kudos to the OP for coming up with such a cursed distraction neat idea!
Appropriate Skills: Endurance, Perception, Religion, Streetwise
Unlockable Skills: Athletics, Stealth
Forbidden Skills: Diplomacy
The challenge: Today is one of the largest festivals in the city's history, a feastday of the local churches, where the faithful fill the streets in revelry... all in the name of their deity of choice, of course. One of the traditional events during this party is the cross-city race, where teams try to make it through the packed roads from one side of the city to the other in the shortest amount of time. The winners are recognized by the City Council for their resourcefulness, and may be called upon in the future should anything arise that needs to be dealt with. The losers... well, at least there's plenty of ale nearby to console themselves on their loss.
Difficulty: 8 successes before 4 failures.
Endurance: This is a grueling race, and plowing your way through throngs of somewhat-sloshed partygoers takes its toll on the body after a few blocks. It allows you to "tough it out", wading through the crowd as you strive to make progress toward the far side of the city. Succeeding on this check will allow for a +2 bonus on future Athletics checks (once unlocked) since pushing your way through the crowd and bouncing off other people is quickly becoming second nature for you.
Perception: While the streets are normally packed shoulder-to-shoulder with the city's residents, occasionally there's enough of a shift in the sea of bodies to spy an opening - whether it's a clear path on a sidewalk, or falling in behind a wagon as it clears a path through the mass of people. Either way, you've found an opening that makes progress significantly easier for a short period of time. Succeeding on this check will allow for a +2 bonus on future Streetwise checks, since you've got a keen eye out for convenient opportunities to get ahead in the race.
Religion: This is first and foremost a religious festival, and knowing the local churches and how they party gives you a bit of insight into which areas will be the least crowded, and when. This unlocks the Athletics skill, which lets you hustle in front of parades and processions while causing your opponents to be cut off by the same displays of faith and fun.
Streetwise: Sometimes, how you get to a place is all about knowing the side alleyways and unused paths. While they may be filthy and vagrant-infested, that's all the better reason for you to go that way... the dirtier it is, the less of a chance it will be crowded. This unlocks the Stealth skill, which lets you dart down a convenient side street without your opponents noticing it, and forcing them to take a longer route.
Not usable - Diplomacy: Most of the people standing between you and your goal are either somewhat intoxicated, or have scouted out that precise location on the sidewalk since before dawn to have a better view of an upcoming parade of holy relics. Taking the time to sweet-talk them out of your way just isn't feasible.
Results
Success: The City Council recognizes the group as the victors in front of a raucous crowd, gaining the team celebrity status in the city for the time being. In addition to the purse for winning the race, members of the Council may further (and more privately) recognize the group's skill by contacting them for help on future matters.
Mild Failure (5+ successes): While the team did not win the race or the prize that came with the victory, they did manage to impress enough people on the Council that they still might be sought out for help.
Moderate Failure (2-4 successes): You lost, and by a considerable amount. You can still fade away into the crowd without too much ridicule for your performance.
Total Failure (0-1 successes): Not only did you lose, but you did so in an embarassing fashion. Perhaps you never made it to the finish line, or maybe you unfortunately found that overturned cartload of manure on the way there. Regardless, the group is heckled for a while in the city... at least, until they prove themselves to be better than that.