Well the street race challenge would be a series of 8 races taking the top two from each race to bring their street racer to a final challenge. This would declare them best champ, and they get a prize of their choice. Something like that.
EDIT:
Also you'd have decide a vareity of things like: tires to be used, PP, HP range and assist they can use. I'd say for them to use none. You can get further into how many laps will be raced, damage setting, or tire and fuel wear. If you want clean racing or a bit rough but not too outrageous.