Our first hotel in Ha Noi looked out over a little lake. In the middle, on a small island, is the Turtle Tower. The tower was built in 1887 to commemorate a 15th century Vietnamese hero. At that time France occupied Viet Nam, and, shortly after the tower was built, a copy of the Statue of Liberty was sent from France for an exhibition. The French decided that their new statue would look great on top of the tower, which I'm sure the Vietnamese didn't appreciate, but there it stood until the French were ousted in 1954. (In a bit of irony, the tower commerates Le Loi who is revered for driving out the Chinese.)
Visiting Ho Chi Minh's mausoleum is one of the 'things to do' during your first visit to Ha Noi. His body had recently returned from Moscow where the embalming had been spruced up. Frankly it looked more like a porcelain figure than a person, but the grounds were interesting.
The mausoleum is adjacent to the presidential palace which was built by the French in 1900. After the French were defeated in 1954, HCM symbolically declined to take up residence in the palace. In the beginning he lived in a small caretaker's cottage on the palace grounds, but for his permanent residence he asked that a stilt house be built nearby. The house is an elegant version of traditional Vietnamese house architecture. It's modest in size, but looked very comfortable.
Another 'must' is a cyclo ride through the old section of the city.