For the "No Claims Bonus" award, you need to drive for 5/10/20?/30 consecutive minutes without damaging your vehicle. You can easily just go into a solo session and go to the horse racetrack along the East side of the city and drive there for 30 minutes like I did (very boring...).
I'm sure there is also somewhere where you could just tape down RT, and rubber band the vehicle for 30 minutes, but I wanted to make sure I knew I didn't crash. Honestly, I only recommend going for this one if you want to get all the platinum awards. You can easily find 30 much less annoying awards to get, and this one doesn't even give any kind of other award.