There are several day trips I would recommend from Cape Town, and with car rental in South Africa being both cheap and easy, there are many possibilities for exploring the surroundings of the city. The hardest part is usually getting used to driving on the wrong side of the road, but after the first few kilometers this usually isn’t a problem. If driving sounds scary, there is always also the option of taking the train/Metrorail or just jumping on one of the many share cabs/minivans which are used instead of local buses.
If you want to go to relax at the beach and are tired of touristy Camps Bay, or just want to catch some good waves for surfing, then Muizenberg is a good place to go. It can be reached in about a half an hour by car from Cape Town, or a bit less than an hour if you want to go by Metrorail/train. Here it is also possible to rent surf gear, plus you can buy some cheap and good ice cream by the beach. This is also where you can see the famous colorful beach houses.
If you are interested in hiking, Cape Town also offers some excellent trips that can be done in less than a day. Then I would recommend starting with Lions Head (easy/just a couple of hours), then go up table mountain and take the cable car or rappel down (medium/almost full day) or cross all the Twelve Apostles (hard/several days). You should be able to see all the way to Robben Island from all of these places and get a great view of Cape Town.
Stellenbosch and Belleville are also places I would recommend as day trips by car or train, but as these places are known for good dining and wine tasting, it might be smart to take the train. It is then important to bear in mind that traveling by train at night is not advisable, so if you are planning on returning late it might be better to spend the night or order a taxi for the way back to taxi. We had to chose the latter when going back from Belleville, and the taxi bill grew pretty large compared to the few rands we had spent on going there by train!
But the ultimate daytrip from Cape Town is to go south to Cape Point visiting places as Fish Hoek and Simons Town/ Boulder Beach along the way. I’ll write an own post about this coming up in a few days..