Has anyone ever ran a fair, or games during any of their campaigns? any ideas for games for the magic user in the group?
I've rarely seen these things go well, I'm sorry to say.
In one campaign, we were all excited to go to a 'joust' with a lot of competitions. They boiled down to single-elimination rounds with a roll per round, just with tons of modifiers. PCs mostly got knocked out the first round due to a few bad rolls. One went a few rounds and won a side-bet with an NPC rival who went one round fewer. The rest was the DM determining which NPCs won each event.
Somewhat more fun was the dwarven drinking game "I'll Kill You!" Which amounted to a series of FORT saves leavened with extravagant death threats.
Going back further I recall DMs handling games of chance and contests with a roll behind the screen. ( "I'm going to join the dice game" :rattle: "You lose 6 gp." )
Of course, you can just run an arena duel or battle as a combat. That worked out well, later, for the same DM who ran the disappointing joust, above.
But where he really pulled it off was a chariot race. I don't remember all the details, but we had our minis out on plastic bases, two to a base to represent the chariots, and they edged forward or fell back each round as a sort of leader board, rather than actually moving around an elaborate track. Each round, there were random 'complications' that you could avoid or leverage using a choice of skills to pull ahead, and/or you could attack other drivers, ram chariots together, or whatever you could think of. It was 2 characters per chariot, so there was both intra party competition and competition with NPC rivals - and a political element, because we were trying to curry favor with the local nobility.
I'm sure your could run something like that by dressing up the chase rules. Make sure everyone watches Ben Hur, first.
I don't think I've ever seen a satisfactory archery contest. Bounded Accuracy would make it a fairly random event.
It might go better leaning more heavily on narrative instead of making a lot of checks. Narrate success in early rounds and describe a capable rival winning several matches, before bringing in the dice, for instance.