Agree with invisible, being vigilant about your belongings is a must. It is safe there but if you are lax with the way you handle your belongings it could lead to theft.

My Viet wife and myself always use the gold shop "Dntn Vàng Hà T m" on the south western side of Ben Thanh Market. Easily findable on Google maps.
They are very busy and were offering 800 dong per Aussie dollar better than the airport that's an extra $20 per $500 changed.
That pays for a very good restaurant meal