Find the busiest intersection (the roundabout near the markets is a good one). Buy an iced coffee, pull up a banana lounge, watch, and ready yourself for the involuntary ooh aahs! It is illegal to carry more than two adults per bike, but a family of six is no problem.
Cholon's Binh Tay Markets are far better than the touristier Ben Thanh. Get in amongst the hustle-and-bustle. Be on the lookout for the Vietnamese coffee makers. They make a great, unique gift that won't result in excess baggage charges.
The War Remnants museum reminds you that there are two sides to every story. It gives a new and unknown perspective on what led to the "American War."
District 1 is geared heavily towards tourists and gives a false impression of the city, as it is thick with touts, postcard, and book sellers, all pushy but good natured.
Quick Tips:
The best advice I was given before arriving was to walk slowly into the traffic and just keep walking; don't stop, run, or swerve.
The best exchange rates were at the Saigon Jewellery Company during the week. Travellers cheques are next to useless and ATM's have a very low daily limit.
Don't pre-book accommodation, as even pre-paying doesn't guarantee a room and you can always haggle an unbelievably low rate in very modern, clean three-star hotel.
When you are looking at heading out of the city on day trips, don't for a second think it will be cheaper easier to do it yourself. Head to De Tham Street in District 1 and pick a tour. Trips to the Mekong, Chu Chi tunnels, etc., are incredibly cheap in air-conditioned minibuses.
Avoid the T-shirts, as thousands of nylons died in their manufacture and an XXL equates to a medium
Best Way To Get Around:
Taxis are plentiful and cheap. Find a driver you like and negotiate a half- or full-day price.
Once you get used to the rhythm of the traffic, it is a very easy/pleasant city to walk around.
Don't be tempted by the moto taxi, as 56 people a day die on Saigon roads, or so the English-language paper reminds you every day. If you wouldn't get on the back of an under-powered, under-braked motorbike with a total stranger at home, why would you do it in a third-world country with a third-world health system?