I went in Aug 2003 for 3 nts and stayed at the Sofitel Metropole. Decent hotel and amazing breakfast. Was able to get a tailor made Vietnamese dress in one of the main shopping streets over-night.
You can see Ho's tomb but it's not always open. When we went, it was closed so you'll need to check. You can also do a day trip to Halong Bay through one of the tours establishment along the street or from the hotel. It's an early start and a very long day though. I think the drive was about 3hrs each way, or something like that. We gave it a miss as were completely exhausted after flying straight from Sydney - Hong Kong - Hanoi.
There's a lovely lake which you can walk around. Great place to buy hats as they are dirt cheap and some are very nice although rather on the small size so I only bought kids ones. Nice hand-made shoes where you can actually choose the style of strap to go over the sole. they just nail it in and you have a slip-on. Pretty cool! and pretty.
You can take a tour of Hanoi on a cyclo to see the town and then decide where you want to stop for shopping, a meal, etc. This would be a good way to see the French quarter. The street shops are amazing. You'll come across a whole row of shops selling just bamboo, shoes, hats, lanterns, clothes, souvernirs, etc. Great fun! Enjoy.