I did a one-day tour through Ann Tours (highly recommend Tony and his crew). Nice car with driver and guide. Saw the following and while we moved fairly quickly, I didn't feel rushed. It was a good overview of sites for someone with limited time. Guide spoke fairly good English and was very knowledgeable about the history of the city.

Opera House
Continental and Rex hotels
People's Party Bldg (Hotel de Ville)
Notre Dame
Post Office
US Embassy
Presidential Palace

Lunch break

War Remnants Museum
China town and Binh Tay market
Thien Hau pagoda
History Museum (quick look)
Emperor of Jade pagoda