There are plenty of ways to get around HCMC without a car - in fact, owning one can be inconvenient due to lack of parking in the city. The city's chaotic traffic also does not make for a pleasant driving experience.
Taxis and motorbike taxis are two of the most popular ways to get around HCMC, and there is also a comprehensive bus system.
See Getting Around Ho Chi Minh City for more.
Best of luck with your move.