As you do not mention clearly about your travel time as well as your budget condition, so we can only give some general advices.
To travel to Ho Chi Minh City or Saigon, you need to have enough money for these main spendings: transportation, food, accommodation and entrance tickets to tourism destinations, not to mention your spending on shopping and other unexpected fees.
Saigon is such a big city that in order to visit all of the most well-known tourism destinations, you need at least two or three days.
Normally, the minimum budget spent for accommodation will range from VND 150,000 to VND 300,000/day, depending on the quality of the hotel and its location. Public transportation is quite cheap, which will cost you about VND 50,000 to VND 70,000/day if you move around inside the city. However, if you choose taxi as a means of transportation, the fare will be about VND 11,000/ km so each journey will cost you VND 50,000 on average.
As every other city and province in Vietnam, Saigon is a heaven of street food. If you do not mind eating like the locals at street vendors, you will only need to spend about VND 100,000 each day to have very good meals. The ticket for museums will take you about VND 10,000- VND 30,000; while most of other tourism destinations like Notre-Dame Church or Central Post Office have free entrance.
In sum, if you want to travel on a shoe string, you can do so with only VND 1.5 million (or $75) for 3 days in Saigon. $120 will probably give you mid-range hotel and more flexibility with travelling. For top hotels and sit-down restaurants, expect your budget to start from $500 for 3 days in Ho Chi Minh City. You can also refer to our guide to cost of living in Ho Chi Minh City for further information.
We hope this helps!