We didn't do anything too adventurous. Still, I'd suggest the following (in no particular order):
1. Watch a water puppet performance. We went to the one at the History Museum.
2. Eat, eat, and eat, at the hawker stalls in the markets, at the many restaurants... The food is cheap, fresh and tasty.
3. Shop at the many small boutiques in the Dong Khoi area. There is lots to buy, from embroidered bags to pretty dresses.
4. Visit the War Remnants Museum. It's a sobering experience.
5. Do the Mekong Delta tour, for a breather. HCM can be overwhelming.