The central French Quarter is small and walkable — most of the colonial-era sights are within a fifteen-minute walk of the Opera House. For trips further out (Du Hang Pagoda, Hang Kenh Communal House, Bến Bính harbour), the easiest option is a Grab car or motorbike (the Vietnamese equivalent of Uber, used by almost everyone).
City buses cover the main routes but are not used much by visitors. Cyclos (bicycle rickshaws) still operate in the old streets and are a slow, characterful way to see the colonial quarter; agree the price before boarding. Bicycle rental is available at a few hotels and is excellent for an early-morning circuit of the old town before the traffic builds.
For day trips out of the city — to Cát Bà, Đồ Sơn, or the Bạch Đằng River — hire a car and driver for the day, which is cheaper than it sounds: around twenty to thirty US dollars for the whole day.