There is only limited parking available at the Blackweir Tavern (which is Race HQ) so it is advisable to use the nearby pay and display facilities. These are situated further along North Road (A470) heading towards the city centre and in this direction, the car park will be on your right.
However, given the traffic conditions at this time of the day, the car park is best accessed travelling in the opposite direction, i.e. away from the city centre. You will then be able to turn left off the road into the car park.
If you arrive on North Road heading towards the city centre therefore, pass the car park on your right, turn left into Corbett Road, first right into King Edward VII Avenue and turn around. Turn right at Corbett Road traffic lights to put you on the left side of the road for the car park.
Cardiff Council car park website (click the City Centre drop-down)
Parkopedia site for North Road