As with every country in the world, when you arrive at the airport you are at the most vulnerable. This is because generally travellers carry cash and quite a lot of it as well. Therefore care is always needed and advised. Vietnam is a very safe country we have never had a problem, however we always take the most precautions when arriving at any country especially if it is on business.
In Ho Chi Minh the ride is very quick, taking between 10 to 30 minutes tops at most times. The cost of a car will be between US$ 10 – US$ 25. Depending on the hotel.
Hanoi however is quite a bit further, and can take anywhere from 30 minutes to one hour depending where you are staying. The cost here is considerably more between US$ 20 – US$ 50.
From the airport never take a taxi from a tote. This is difficult to define in either Ho Chi Minh, or Hanoi, so strongly recommend that you take the comfort, luxury and safety of one of the above, hotel cars.
Within the city, the taxis are safe, and pretty many hassles free. Meters run in most of them, although the starting rates vary a little from each taxi company.
Bicycles can be rented out for around US$ 1.5 per day, they are a bit wobbly, but good fun and a great way of travelling around.
Motorbikes are between US$ 4-7 a day, although I will let you decide whether insurance is included.