Hi there,
I went backpacking with DD through Vietnam in 2005 when she was four. We spent a month out there and had a brilliant time.
I'd definitely recommend Hanoi above Saigon. The city is more beautiful, there was more to do with DD and I'm somewhat biased against Saigon because I got mugged there
We stayed in the Sofitel for the first few nights (not the Metropole but the other one) but after that, we did the usual backpacker kind of thing. Most places we stayed at were a double/twin room (I'm a lone parent so it was just DD and myself) ensuite and with breakfast included, all for around $10 per night (though that's probably gone up a little by now).
The Water Puppet show was brilliant. We had front row seats and DD adored it. Word of warning though, douse yourself in DEET before you go in as there are zillions of mosquitos buzzing round the water and I got bitten alive (though DD has still never had a mosquite bite in her life )
We also went and saw Ho Chi Minh's body lying in state in the Mausoleum - there was a special viewing platform for children and it was a really good place to see. DD was fascinated. You'd need to check the opening times though, as it only opens around once a week IIRC and also his body is shipped to Russia or something once a year to be tweaked and adjusted before returning to Vietnam.
The Vietnamese were very friendly and it was easy to find childcare if I wanted an evening out. There were lovely women in hotels I stayed in who would read to DD and get her to bed whilst I went out for a few hours.
Halong Bay was an amazing place. It's about a half-day bus ride from Hanoi. We stayed on a boat overnight and the scenery was astounding. We swam in the sea, toured limestone caves and met other backpackers on the trip.
Hoi An was another really good place to stay. It's a couple of days' travel from Hanoi by train. We took an overnight sleeper from Hanoi to Hue, then a bus down to Hoi An. The beaches were beautiful, the architecture was brilliant and the town is full of tailors who make up clothes for you for a brilliant price (I got lots made for DD and I and shipped them back to the UK).
DD and I also travelled down to Nha Trang and then to Saigon, but the highlight of the trip for us was really Hanoi and Hoi An. Hue was interesting if you're into the Vietnam War (I'm a complete war obsessive and wrote my dissertation on the subject so dragged DD round war sites and into tunnels etc - fascinating stuff!)
Hope you have an amazing time! DD has typically forgotten most of the trip since she was so little when we were out there, so will have to go again!