Do not take the below as an advice. We are just sharing our experiences.
Taxi service: Uber. Works well, but when we ordered a taxi to the airport on our way back, the driver tried to blackmail us. We were lucky to have enough time to order another Uber.
Rent-a-car: we used Rent a cheapie https://www.rentacheapie.co.za/ . We had no problem with them. Book ahead of your trip, good cars may be already booked. We purchased an insurance, it was not a big part of the cost, but gives relax.
Driving: always close the doors. The driving wheel is on the right, which is unusual for Europeans, but there is no problem to get used to it.
Security while driving: there is a phone number on a visible place (on the windscreen in our case) which probably you have to call, if you have a problem on the road. Ask how it works exactly this when renting the car.
Sleeping: we slept in Bloubergstrand – a district of Cape Town that sits directly on Kite Beach. We used Airbnb to book it and had no problem with it. There are several supermarkets around, and good restaurants. There is a mall in close proximity and several kite/surf shops. We still used the car to move around the district. Eden is another place popular with foreigners.
Kite sports we’ve visited: Kite Beach, Misty Cliffs (one hour drive south-east), Hermanos (search it on the map). There are different conditions around Cape Town, so good to find a local advice where to go. If there is a cloud on top of Table Mountain, expect serious wind.
Kite sizes: have small ones! 90 kilo kiter needed 5 m2, 7m2 and a bigger kite for lighter days. We are riding waves, so for jumps probably prepare bigger.
Where to go, what to visit – probably Trip advisor will have all you need to know. Cape of Good Hope and Cape Point is a must. Book the visit in advance.