I have not been to Hoi An but have been to Hanoi an HCMC. I absolutely loved Hanoi where I found it to be a mixture of old customs and a little bit modern (not too modern like HCMC).
I found a tour called Awesome Vietnam Travel who did food tours walking through the city. They were absolutely great. The manager also offered to pick us up at the airport and said he'd just get the $25 bucks when we did the Food on Foot Tour. In Hanoi, get up early and go to Hoam Kiem lake. It is a fabulous site with everyone exercising or dancing. Any form of movement constitutes exercise. My favourite was seeing a large line of about 30 middle age ladies standing behind each other and slapping the person in front of them's back.
In Hanoi we stayed at the Hotel Metropole and it was fabulous. Steeped in history with courteous and very helpful staff and close walking distance to many fun sites around the city.