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A rare gem and a must see for geology & natural history enthusiasts. This 3-story building houses a collection of earthly artifacts (and even some non-earthly ones), including a few rare examples. Sadly in a state of neglect with poor lighting and little to no interpretive text. You can read more about it here.
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The museum has a fine collection of Vietnamese antiquities. Read up on Vietnamese history first or you'll have no idea what you're looking at. Outside, the Botanical Gardens are very nice and a good place for a cheap lunch away from the crowds. Six times a day, you can see a 20-minute water puppet show (adult 50,000 dong, child 35,000 dong). It's quite amusing, even for adults.
A museum detailing the life and achievements of politician Ton Duc Thang, known for his role as president. The first floor has a special exhibit (as of February 2018 about his time on the infamous prison island of Con Dao) and the second floor has a biographical display featuring artifacts, dioramas, and photographs telling the story of his life; there is also a painting gallery.
Nhà thờ Đức Bà or Basilique-Cathédrale Notre-Dame
A French-built Catholic cathedral in the city center.
Nhà hát Thành phố or Opéra de Saïgon
An opera house built by the French during the colonial period, and without a doubt one of the finest performance venues in Southeast Asia. In modern times it is home to the critically acclaimed AO show, an acrobatic show that fuses Vietnamese traditions with modern Cirque Nouveau performances. Occasionally hosts classical music performances when the AO show is not being performed.
One of 12 mosques in Ho Chi Minh City, the Central Mosque was built in 1935. It was constructed for worshipers from southern India then resident in Saigon, but now Muslims from as far as Pakistan and Indonesia come to pray. Friday has the biggest congregations. The shaded veranda and cool stone floors make it an ideal place to sit, read, or even nap in the heat of the day. As with most mosques, remember to take your shoes off before entering and dress conservatively if you wish to enter.
Built as the Hôtel de Ville, it's a striking cream and yellow French colonial building beautifully floodlit at night. No entry, but the statue of Uncle Ho in front is a very popular place for photos.