The sun-flecked ocean glittered to the west as I wound my way down Victoria Road in Cape Town toward The Twelve Apostles Hotel and Spa. The origin of its name would quickly become apparent — from my position on the coastal road it was easy to see the distinct craggy peaks called the Twelve Apostles jutting up one after another, forming a long spine down the Atlantic side of Table Mountain National Park toward Hout Bay.

I passed the hotel’s friendly resident cat on my way up to the hotel’s Leopard Bar, where I shook hands with Nardus Buys, the head concierge. We took a table with a pristine view of the Atlantic and I explained that I needed help: I was having difficulty spending money. Low prices and a strong dollar meant that I struggled to find pricier experiences that would interest a more profligate spender than myself.

Mr. Buys generously offered his assistance. “If I can plan an itinerary for someone and make their stay in South Africa memorable, there’s nothing more satisfying than that,” he said. He drew up a daylong itinerary for a fictitious traveler on a budget of $1,000, or about 14,000 South African rand. I would then take that itinerary and, keeping its general spirit, remake it on a much more modest budget of $100.