The street races and midnight battles are straightforward races, much like the usual exhibition races. However, a total of 50 wins in head-to-head races are required to unlock every street race, which can take some time if you don't speed it up like I did.
Go to the airport in the outback part of the map and challenge a drivatar that is heading west (left when looking at the map) that is also past halfway down the runway. At this location the end point will be on the side road next to you. Cut across the gap between the roads and you can often finish in around 5-10 seconds.Here is a video tutorial: