We stayed at a place called the Yellow House in the main part of the city- I do not recommend this place- very loud at night with lots of backpackers and fixtures coming off walls and doors. We only stayed 2 nights and then left to go to Danang, but would have found new accommodation otherwise.
While in Ho Chi Minh, all we did was go to the Cu Chi tunnels and to the War Remnants Museum. I recommend both of these things if you go to Saigon.
The Cu Chi tunnels are outside the city aways, we took a bus trip with the place the hotel booked us through which was fine. The tour was not long, but you get to climb in the tunnels that were used by the Vietnamese during the war as escapes and hiding places. Contrary to the statement that the people lived in these tunnels during the war, our guide informed us that this is not true, and I am inclined to believe him- the tunnels are too cramped and small for anyone to live in- an average person cannot even turn around in them- it's one way out for us taller people- and yes- I fall in to that category.
We also went to the War Remnants Museum (the tour from Cu Chi Tunnels will drop you here on your way back to town if you want, then you can make your own way back to your hotel) and so we wandered around this for a little over an hour. It's obviously got a different slant to the war in favor of Vietnam, but I think I still learned more about this war in my time here than I ever did in school. The atrocities in war are both expected and surprising, and they spared no feelings when they created the displays here- photographs of victims and stories create some distant mental images of what occurred here.
From Ho Chi Minh, we fly to Danang. It's really inexpensive to fly on Vietnam Airlines if you book more than a week in advance and saves you a lot of ground travel time. If you are going to stop along the way, I would do it in your journeys in Southern Vietnam, as there are a few towns that friends recommended as nice stops along the way, whereas from Hue to Hanoi (the northern half) there were no recommended stops from anyone.