Personally, I would love a recreation of the "Trans-stellar Rally" from the Voyager episode "Drive", with various hazards that you would have to either dodge around or else plunge through (plunging through them would be a shorter distance, but you would be in an environmental hazard that would force a Red Alert and thus prevent you from using the Full Impulse setting. Proper use of speed-boosting abilities would still let you come out ahead of going around the hazard zone though).
How many Starfleet Engineers does it take to exchange an Anti-positronic Photon Emitter?
I would love it if they added an Ice Rink and Race Course on Andoria.
And the shuttle races, people been wanting that since before Shuttles were even added to STO. I could see a race course similar to the one on Voyager (maybe take some ideas from the race episode of SG-1).
Then to keep things fair (like Winter Wonderland), abilities are disabled to prevent everyone from having advantages like Emergency Engines or using Evasive or Deuterium.