The right option for most tourists, like you who have just arrived, is to check in at a hotel, and the first port of call should be Saigon Notre-Dame in district 1.
A large cathedral in Cong Xa Paris Square in downtown Ho Chi Minh City, it is a real landmark and it is a quick in and out trip. Short and sweet and of course free. Next up should be Reunification Palace on Nam Ky Khoi Nghia. For a small fee of around US$3 you can visit the former home of the President of South Vietnam.
Not only is it a journey back in time, but you get a wonderful view of the tree-lined Le Duan Street, making its French design obvious.
A short five-minute journey from there is the War Remnants Museum, which is not for the fainthearted. The horrors of Agent Orange and US bombing missions during the American War are evident and hard-hitting. A very sombre trip, but one which I think all tourists to the city must make, if they have any interest at all in the country they are visiting.
From there you can head down to Cach Mang Thang Tam (August Revolution) Street in District 3 and the new statue of Buddhist Monk Thich Quang Duc, remembered for his self-immolation to make a political statement about the treatment of Buddhist Monks in the early 1960s.
If you want to see the Chinese part of town, from there it is a short journey to Cho Lon (big market) in District 5 and 6. There you’ll find the former premises of the Le Grande Mondial, the most profitable casino in the world during the 1950s, and straight up the road from there is St Francis Xavier church (Father Tam church) on Hoc Lac Street where former President of South Vietnam Ngo Dinh Diem was captured during the military coup in November 1963 before his execution.
After all that history you will want to relax a little, so head to Saigon Pho 2000, ideally located next Ben Thanh Market downtown, for a bite to eat. Then you can do a spot of shopping and wheeling and dealing.
There are of course both high-end and low-end shopping facilities located all along Le Loi Street and cafes aplenty for your downtime.
The Rex Hotel is the most famous location in the city. It was a popular haunt of journalists and US servicemen during the American War.
The top floor restaurant and bar is a must for any visitor to Saigon. There is live music, among all your other necessities, but it is more than that. You can feel the history as you sit there with a nice view of the city.
Of course, you can be bold, forget about the city tour, and instead go to the popular Cu Chi Tunnels - buses run regularly or you can hire a motorbike and take the two hour journey there. Word of warning, though, it can be dangerous if you are inexperienced on a bike. The great thing about this part of the nation’s history is that it has been turned into a fun area with groups of Vietnamese and foreign tourists alike taking in the historical aspect and having a picnic at the same time, with a lot of green areas in the complex.