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Hello Stella...

Upon arrival at Tan Son Nhat Airport,  if u had to use a taxi...go for Vinasun taxis.

Hello I am Nhi and living in HCM city . If you need, i will do tour guide in here for you 
let's you feedback for me soon
Hope i can meet you in SaiGon

@Fongecee: thanks for the info. But is there any coach bus or airport express to the city that I can take ? If so, how long does it take me to the city near Ben Thanh . Cheers

La Stella...Take a taxi as suggested.  Vinasun is perhaps the better of most.  About 100,000 VND from the airport.  Some will charge you more.  If you really want to save and go by bus the no. 152 runs to the Market for about 10 to 15,000 VND for bags and person...until 6 pm.
A good 20 minutes to 30 by taxi (4 wheel), depending on traffic; not sure how long by bus.
Looking for tour information...I've done business with Sta Travel at 27 Thu Khoa Huan street, just on the other side of the Market.  They have always treated me well..also some fair hotels nearby.
Hope this helps.
Good Luck and enjoy

Hi Stella,

Anthony has the perfect response for you. I never had the chance yo explore the bus option since my company insists on using the cabs. Oh if you do use the cab there is additional 10,000vnd (usd 45c) on a receipt that the airport attendants passes to the cab driver which is not reflected in the meter.
I heard that there are big rooms in District 3 Ngyuen Trai where it costs less than 400,000 per nite.

Fongecee...Good note to pass on...I forgot that part...I usually walk out and get a bike into town.  Even when using a cab, I walk out to the gas station area.

Hi Stella,

You can take bus 152 from airport to Benh Thanh market. That's what I did before. It's cheap and efficient if you don't any big suitcase. Here are some more info from tripadvisor for your reference :-

"The cheapest way is to take public city Bus # 152 parking in a lane few steps away on the right side from the Arrival's entrance.
It takes you downtown to the Bus Station on the opposite side of the traffic round about from Ben Thanh market, at a cost of 6,000 dong + 6,000 dong if your luggage weighs 10kg or beyond. It runs every 20 minutes from 6 am until 6 pm."

Simon

Welcome to Viet Nam Stella,

You can take a taxi from the airport to Distrist 1  about 100.000-150.000 VND, you can stay at the hotel near the Ben Thanh market. If you need anything or help just send me an email. ***

Hi Nhi, that's very kind of U to be a guide for me in the city . Would be great if U could go on the day tour & show me around .

Please , PM  me & discuss for the further info.

Cheers