Amer Fort (also commonly spelled "Amber") is a defensive palace built by Maharaja Man Singh I in 1592 and has long been the capital of Jaipur. The fort is carved high into the hillside and can be reached by a steep hike or by shuttle bus from the city below (better yet, let the elephants do the work). Highlights include the first courtyard, Jaleb Chowk, with many decorated elephants, and the Shila Devi temple dedicated to the goddess of war. Also noteworthy is the adjoining public auditorium (DiwaniAm), with its beautifully decorated walls and terrace frequented by monkeys.
Other highlights include Sukh Niwas (Hall of Joy) with its many flower beds and passages once used to carry cooling water, and the Temple of Victory (Jai Mandir), known for its many decorative panels, Colorful ceilings and great views of the palace and the lake below.
Just above Fort Amer is Fort Jaigarh, built by Jai Singh in 1726, with an imposing watchtower, a fortified city wall, and the largest wheeled cannon in the world. Be sure to take the time to wander around Jaipur's Old Walled City, where there are three fully restored gates and beautiful bazaars, as well as the charming City Palace, a massive edifice made up of courtyards, gardens, and clusters of buildings.