The Aina Mahal palace, or 'Hall of Mirrors' was built during the flamboyant rule of Lakhpatji in the middle of the 18th century and is very beautiful.
It also houses a handicraft museum where the crafts from various parts of Kutch is put. The Aina Mahal is at the northeast corner of Hamirsar lake, easily walkable from most of Bhuj. Anyone along the way will give you directions. Be sure to explore the rest of the compound outside the palace, with its beautiful carved doorways, elaborate window boxes and balconies. Most of the compound is in ruins, some brought down as recently as the 2001 earthquake. Poke around and explore unexpected places; don't settle for just walking into the palace museum with a ready-made experience.