It’s the signs that flash past you as you’re driving that remind you you’re in Africa, not San Francisco or the south of France.

It’s an easy mistake to make. There’s the slatted, wooden, low-rise architecture of San Fran, the wind-bent trees battered by years of ocean squalls into makeshift weeping willows that you see on Highway One. Then there are the splashes of colourful flora, the jaggedly beautiful cliffs looming over meandering seaside drives. This could be the foothills of the Alpes Maritimes. I could be in my convertible, on my way to Monaco for a spot of lunch with a young Grace Kelly.

But the signs, they tell a different story. Every building you pass bears the seemingly compulsory pronouncement “Armed Response”. Big blue notices warn you not to feed the baboons. Why would I want to feed a baboon? It’s not like I set off on road trips with a picnic for two – me and a baboon. I’m off to meet Grace Kelly, not Cheetah. (I know, I know, Cheetah was a chimp, but there aren’t any famous baboons.)

Apparently (and I’m really not making this up), “baboon-jacking” is a real risk out here. If you’re not careful, the hairy bastards will have you out of your vehicle and will be using it as a public restroom.

I’m on my way down to the Cape of Good Hope. I’ve hired a gorgeous black BMW 330ci convertible for a price that would get me the limited use of a Reliant Robin in the UK. This country is so cheap, it makes you unbelievably angry at how much we have to pay for stuff back home. Mustn’t get angry. I won’t be able to deal with a baboon-jacking if I get angry. Stay calm, stay cool, the baboon respects coolness. Wasn’t King Louis in The Jungle Book a baboon? He was cool. No, I think he was an orang-utan. Ah well, close. Think happy thoughts...

I’m driving solo down the Atlantic seaboard of South Africa – the roof down, listening to the Killers and on my way towards a fabulous seafood lunch in Simon’s Town. It’s apparently the home of the South African navy. Don’t know much about the South African navy. Can’t think of any of its great naval victories offhand. In fact, I can’t think of anything about it. Ah well, that’s what travelling is all about. I’m here to learn, not just to enjoy myself. Still, have to admit, life doesn’t get much better.

Look, more signs: “Penguins 500 metres ahead.” Penguins! I’m in Africa. Baboons I can understand, but penguins? Oh I get it. I bet it’s one of those clever promotions for a new Hollywood kids’ film. Why do they make so many movies about penguins? You never see anything about the... ostrich, for instance. Oh my God, I must be psychic, there’s a bloody enormous ostrich on the road in front of me. Perhaps someone put something in my biltong. This is turning into Fear and Loathing in Suid-Afrika.

No, it’s not called that any more, it’s the Rainbow Nation. Everyone’s all equal now, and there aren’t any nasty racist Boers telling people to get off benches. Everyone can do what they want... as long as they can afford it... which most black people can’t... but if they could, they would be free like the whites... free to build enormous fences to keep fierce dogs behind in fear of... them... the black... no, the free ones. It’s complicated, and if you try to talk about it with anyone, they all tell you that you “don’t understand Africa”. And that’s that. Happy thoughts...

THERE’S ANOTHER sign: “Don’t feed the ostriches.” Like I’ve got a choice. If that oversized turkey decides he’s peckish, I’m history. No wonder that nobody else is in a convertible. Oh my God, look at that beach. It’s got thousands of penguins on it. There are penguins at the bottom of Africa? Maybe they took a trip from Antarctica, then got stuck here in a bizarre racial dispute in which people couldn’t decide if they were black or white.

It’s so weird actually being here. I’d heard so many things about Cape Town. My grandmother was born in the city and my mother was always telling me how beautiful the place was, despite never actually having been there herself. To be honest, I’d always been a little nervous about visiting. I was loath to discover that my grandmother had been some viciously racist Boer, stalking the veld in an armoured car, brandishing a four-barrelled elephant gun. My mother always assures me that this was not the case, and that we were on the side of the angels. I still have my doubts.

The Lost City, it’s called by some. A European metropolis marooned at the tip of Africa, just waiting to be discovered. “Great shopping, amazing weather, so cheap,” said friends who’d been there. “A dangerous place, everyone lives behind electric fences,” said others.

First impressions were... pretty good. Anywhere that can give me dry 30-degree heat in the middle of December gets my vote. As you descend into the “city bowl”, you notice Table Mountain. This staggering lump of flat rock acts as a 3,500ft backdrop to the whole city. It even comes with a rolling dry-ice show as the almost perpetual cloud (known by locals as the tablecloth) rolls over the edge, as if off some enormous stage. You expect to see a huge 200ft Bono straddling the edge of the mountain, screaming into a microphone and dedicating his next opus to “the CITY BOWL people of Africa”. I’m sure it won’t be long before he manages it.

The town is such an easy one to slip into. Within hours of my arrival, I know my way around. I’m staying in the Beverly Hills area, Higgovale, nestled high on the slopes of Table Mountain. It’s a leafy village of expensive houses hidden behind high walls and spiked fences, and reminds me a little bit of the Hollywood Hills.

From my hotel, it’s a 10-minute walk down Kloof Street into the city centre. On my first evening, I hang out at the top of Long Street, a funky, backpacky area that’s full of life until late into the night. I eat at Mama Africa – crocodile and potato salad. Service is snappy. The following evening, I wander round the Waterfront, an enormous development of malls and restaurants, built on the old docks, which attracts thousands of Capetonians every night. I am in love with this place already.

I start to look in the windows of estate agents, always a bad sign. It’s staggeringly well priced. A posh two-bedroom loft in the heart of the downtown is about £60,000. I start to make plans. Maybe it is a tad dodgier politically than the Cotswolds, but with the money I save on housing, I can buy a bazooka. Anyway, I grew up in Beirut, so this place is a piece of cake.

Days pass, and I can find little to fault the place. The food is exceptional. The people are friendly, the women definitely some of the most stunning I’ve seen anywhere in the world. This really is a little piece of heaven hidden down at the bottom of the southern hemisphere.

BACK TO my road trip – I’m getting close to the Cape of Good Hope now. Last week I was in the Arctic Circle, this week I’m approaching the tip of Africa. More signs warning me about baboons. I decide to put the roof up, better safe than sorry. One of the baboons is laughing at me. He’s probably got a knife. It’s so difficult to work stuff out here. Everything looks so... normal... European and understandable. But I’m not from here, I can’t really judge things properly. It’s okay, but a touch unsettling. Happy thoughts...

Ah, finally, there’s the sign for the Cape of Good Hope. Another world landmark to tick off. There’s the sign: “Cape of Good Hope, the most southwestern point of the African continent.” Hang on. I thought this was the tip of Africa – the most southern point, not the most southwestern point. Everything in “the literature” (the most ridiculous name for a couple of leaflets with pictures of nice baboons on) leads you to believe that two oceans meet here, the Indian and the Atlantic. It turns out that this particular honour belongs to Cape Agulhas, a long way down the coast. You hardly ever hear about it. A tricky place, Africa – it’s wonderful, but you need to keep your wits about you. All is not quite as it seems. Now, where’s Grace Kelly?

Dom Joly was a guest of British Airways and the Kensington Palace Hotel

Travel brief

Getting there: fly to Cape Town from Heathrow with British Airways (0870 850 9850, www.ba.com ) or South African Airways (0870 747 1111, www.flysaa.com ); from £600.

Where to stay: in Cape Town, the elegant Kensington Place Hotel (00 27 21-424 4744, www.kensingtonplace.co. za ) has doubles from £161. Or try the Georgian-era Cape Cadogan (480 8080, www.capecadogan.com ); from £75.

Getting around: Holiday Autos (0870 400 4461, www.holidayautos.co.uk ) has a week’s inclusive hire from £103. Or rent a BMW 330ci for £126 a day, through Book Cape Town (00 27 21 422 5092, www.bookcapetown.com ).

Tour operators: BA Holidays (0870 243 3406, www.ba.com/holidays ) has a week’s fly-drive from £898pp, with flights and BMW-style hire car. Or try Southern Africa Travel (01483 425533, www.southernafricatravel.co.uk ) or Rainbow Tours (020 7226 1004, www.rainbowtours.co.uk ).