Tournaments, Fairs, & Taverns has racing rules. The basic gist is that each section of the race has a target number. Each 'round' of the race (which can be as short as a normal round, or as long as an hour, depending on the scale), you make a Race check, modified by speed and Strength. You add your Race checks together until you reach the target number, at which point you finish that section of the race. If you're doing a chase, the hunter catches up if his total equals or exceeds the prey's total. When this happens, switch into normal initiative mode, and if the prey manages to get away, you keep on rolling.
Basically, calculate each racer's running speed, which is 120 normally, or 80 for short folks. For things like gazelle and cheetah, it'd be something like 240. For each 10 ft. above 100 ft., you get a +1 bonus to your check. Roll d20 + speed bonus + Strength modifier, and keep adding bonuses until you reach the target number.
If you have a head start, you start with a bonus. If the race's "rounds" are actual 6-second combat rounds, every 10 ft. of head start is a +1 bonus. If the rounds are a minute each, you need 100 ft. to get a +1 starting bonus, and so on.
If you want to spice things up a bit, have various hazards, like requiring a balance check every round through dangerous terrain, or a survival check for the hunter to locate the prey if the prey gets too far ahead.
As for the types of critters for that race, maybe gazelle and leopard over a savannah, sparrow and hawk through a canyon, dog and cat through the crowds in the fair, or alligator with wings versus shark with a jet pack.
As for other things to do at a mage fair, well, I've run through a certain adventure that's set in a mage fair, several times. Some nice things included bits of flavor:
* Common folk coming in and paying a few coppers for mages to cast cantrips on them, so that people react to mages nicely. Things like prestidigitation-ing a young lady's make-up, or featherfalling a person as they jump off a high ledge, so they can float for a while. Y'know, fun stuff.
* A group of Dwarvish priests who are trying to convince all mages to give up spellcasting and convert to divine magic.
* A bunch of people are talking about a famous spellcaster who is at the fair, though the PCs never run into him. He's the Great Diogenes, renowned for his brilliant spell-dueling, when in truth he's just a really skilled enchanter who makes people think he's brilliant, and who convinces his foes to surrender.
* A robbery at a curio store gets local guards scrambling around the fair all day, tracking clues and bits of lost trinkets. Worse is that a ceramic egg actually held a minor demon in stasis, and it's been causing trouble all through the fair.
As for mage-dueling, you need some rules. First, a spell: Field of Arcane Courtesy. It makes all spell damage nonlethal within a 60-ft. radius, including summoned creatures, but not normal attacks. And that radius is the area of the duel.
Within the field, you're free to use any spell you want, as long as you don't kill your opponent or cause severe lasting damage. You win if
a) Your opponent leaves the area, or surrenders.
b) Your opponent is knocked unconscious and does not recover within 10 seconds.
c) Your opponent is knocked down two times. (You're welcome to stay on your back if knocked over once)
or d) You counterspell or disrupt three of your opponent's spells.
Tactics that are not allowed include making an illusion of your opponent and having them run out of the arena to make it look like a concession, but you're welcome to Suggest he gives up, or to force him out with telekinesis or gust of wind.
Want to give him some trouble? Have two or three sets of duels, maybe on different days if the fair lasts long enough. Bout one, a normal mage starts off by turning invisible, then summoning a monster to harry the PC in future rounds, and thereafter just fires magic missiles. Rather straightforward.
Second bout, the mage relies on tricks, casting illusions about the field to distract the PC, sending an illusion of himself outside the arena to surrender (to lull the PC into a false sense of security), and then preparing a specialized counterspell to fling the next spell the PC casts back at him.
In the last bout, before the match, a thief hired by the enemy mage steals the PC mage's spell component pouch (give the PC a DC 20 Spot check to notice). See how well the PC fares without spell components.