You know how it is. A few hours under the scorching California sun and your eyes start playing tricks. Even so, an enormous black rabbit in a pushchair was the last thing I expected to cross my line of vision. But then, this was San Diego's Balboa Park.

It's a place that offers surprises at every turn. And what a lot of turns there are. For this is the largest urban cultural park in the USA. I could give you some idea of its scale by prattling on about its 1200 acres, 85 cultural institutions, 15 museums, and so on. But let me put it this way: after entering the park at its northwestern frontier, by the time I reached its eastern exit I was back in Scotland.

Not only is Balboa Park big, it's old. Established in 1868, the park was given a dazzling makeover for the Panama-California Exhibition of 1915. When the elaborate Spanish Renaissance style structures were unveiled, one Spanish diplomat was heard to gasp: "You have out-Spained Spain!" Today, these lovely buildings house attractions that have made the park a magnet for visitors from around the corner and across the world.

Think of a subject and there's probably a museum devoted to it in Balboa Park. From science to sport, automobiles to aerospace, each one offers absorbing exhibits and interactive attractions. I spent a pleasant half hour in the San Diego Natural History Museum taking the world apart on a computer simulation of continental drift. A small boy then put the world back together in the space of a minute.

The park is also home to the San Diego Museum of Art, which has some very fine art indeed. Here, sculptures by Henry Moore and Niki de Saint Phalle rub what I think are shoulders with paintings by Monet, Magritte, and Munch. And if that's not dramatic enough for you, how about The Old Globe? Its three venues stage a variety of productions, from Stoppard and Sondheim to Shakespeare. The 2008 summer season at The Old Globe will include All's Well That Ends Well, so at least you can be sure of a happy ending.

Culture is all very well, but there comes a point when the inner child breaks free. And that point comes at Balboa Park's San Diego Model Railroad Museum. At 28,000 square feet, it's the biggest indoor model railway display in the world. I dare you not to be mesmerised as tiny locomotives rattle their way across the small, but perfectly formed, landscapes. Better yet is the toytown layout, where Thomas the Tank Engine and friends delight trainspotters of all ages.

The park is busy all year round, but some attractions - such as the House of Pacific Relations International Cottages - are open only on Sundays. The cottages - glorified garden sheds, really - represent thirty-one countries. Each has its own decor and most offer refreshments that are more than welcome on a sweltering afternoon. In Iran, I guzzled down some refreshing fruit juice, while in Sweden I gorged on pastries. "Welcome back to Italy!" my host gushed as I returned for a second helping of ice cream. Meanwhile, England was a shrine to the royal family, Denmark was being renovated and France was shut. And then I arrived in Scotland.