The heart of South Kensington is its eponymous Tube stop, which serves the Piccadily, District and Circle lines. As soon as you exit the station, you'll be in a bustling thicket of cafes and restaurants under colorful awnings in a pedestrian zone.
Even on the most dismal of days, outdoor seating will have been set up. It's a defiant gesture, full of hope—a sunny day seems less out of reach when you're sipping a cappuccino outside. (Conveniently, Londoners are impervious to drizzle. Tourists will be wearing ponchos and galoshes while the local population glides by in smart leather shoes and the simple trench. The rain hits them differently, perhaps out of respect for their longstanding tolerance.) June might be rainy and mild, but the good news is, you can find the exact same weather in January, and those cafe tables and chairs will be out at both times of year, standing proud.
From there, you could walk up Exhibition Road and see the looming giants of museums: to your left, the Natural History Museum, often with a long, snaky line full of families; and to the right, the Victoria and Albert Museum, whose floors overflow with design artifacts and art; and just up the road a bit, the Science Museum. You could plan your attack over a strong coffee and a buttery muffin at Muriel's Kitchen.
You're in Little Paris.
Many of London's 100,000 French expatriates have made South Kensington their home. And, because the French took root here, their brasseries, bakeries and bookshops followed, to everyone's benefit. Within a quarter-mile radius you can find the French consulate, French Institute, and the French high school. So, naturally you will find a Cave à Fromage across the street, which offers regular cheese tasting nights. It also serves a sandwich to rival any found across the Channel. A perfect baguette, crisp and then fluffy within, is layered with brie, bresaola, arugula and a touch of olive oil.
After you've enjoyed some authentic, stinky cheese and sauntered down the wet cobblestone of South Kensington (making sure to avoid any sullen teenagers), you could finally venture out to more famous sites like Buckingham Palace or Westminster Abbey. But, it is raining after all. Maybe you'll stay for awhile and take in a movie at the Ciné Lumière. History can wait. You've got Little Paris in London to explore.