Most combat mechanics carry over fairly well to a medieval faire. Typical events would be duels, jousts, and archery contests for the combat inclined. Depending on how prevalent magic is in your setting, you can either have all weapons given a temporary enchantment to deal subdual damage, rather than lethal, or simply provide weapons without sharpened blades for the same effect.
With the joust, you need to decide a scoring system. I like to do the cinematic 1 point for a touch, 3 points for a broken lance, and outright victory if your opponent is knocked off their horse. Touch is, obviously, just a successful attack during the pass. To break the lance, roll more than half damage when you hit (I don't have my books in front of me to see what the damage ona lance is, but if it is a d8, then you'd need a 5, 6, 7, or 8 to break it, et cetera). for a knockdown, force the hit rider to make a Ride check. I've used both DC 5 + the cumulative damage for that joust or DC 10 + the damage of the attack. Tweaks are, obviously required, depending on the level of the PCs.
Your rougish types would likely enjoy games of skill. A mannequin wearing a multi-pocketed coat with bells sewn to it provides a chance for them to work their dexterous skills in fun and mostly socially acceptable way. Simply give each pocket it's own DC to be picked without ringing the bell. Another popular games would be Jacob's Ladder (requiring increasingly difficult Climb and Balance checks to make it to the top).
Bards would likely spend the time trading stories and performing. A competition could even be held (opposed Performance checks).
Mages and Priests are the hardest to find activities for, both because the magic level of every campaign is different and because acceptance of mages varies from region to region, much less game to game. So I'd really have to know more about your setting to come up with any ideas there.
