Start with Kuala Lumpur's vantage points to get a good overview. The aforementioned Petronas Twin Towers feature an extraordinary Skybridge between the twin buildings at the height of 558 feet. You can catch an even loftier view from the Kuala Lumpur Tower (called Menara Kuala Lumpur). From more than 900 feet up, visitors can enjoy truly superb views of the city, except during those hazy days.
Despite the rapid pace of building in the past few years, Kuala Lumpur is still replete with historic buildings offering a sleepier ambience. Royal Selangor Club, representing the city's colonial era and located in Jalan Raja (the city's central area), is one of the most iconic of historic places in Kuala Lumpur. It's located on Merdeka Square, which has a flagpole with a record height. With its lush gardens, King's Palace (Istana Negara) is a regular photo stop during sightseeing trips, though it's not open to the public.
If you're not daunted at the idea of climbing 272 steps (yep, we counted them), Batu Caves is an awesome limestone cave. Discovered and publicized by American naturalist William Hornaday in 1878, Batu Caves has become a popular spot for Hindu pilgrimages. A wild population of monkeys causes an added challenge on the steep climb, as they are very aggressive while seeking something to eat. The site is located eight miles north of the city center. You can get there by train, bus or taxi from downtown Kuala Lumpur.
Visitors dressed conservatively are welcome at the National Mosque (Masjid Negara), an attractive building with a towering 239-foot minaret. It was built in 1965.
Islamic Arts Museum displays a variety of treasures from the Malay archipelago as well as from China and India, including jewelry, textiles, ceramics and armor. The collections are displayed in a unique open layout, which the museum says inspires "a sense of continuity embodied in the Islamic spirit."
Enjoy a walk through the lush Perdana Botanical Garden (formerly the Kuala Lumpur Lake Gardens), which includes an orchid garden, waterfalls, ponds and a topiary collection.
An hour's bus ride from Kuala Lumpur is the mountain retreat of Genting Highlands, one of the most popular resorts in Malaysia. Located 6,500 feet above sea level, Genting Highlands is a bit like Las Vegas -- with an amusement park, the largest show restaurant in the country (often with some of the most famous entertainers in Southeast Asia), and the only place to legally gamble in Malaysia. On top of that, there are several hotels, a water park and golf courses.