The places I've liked the best in Hanoi are in guidebooks but there are certain things that I think make them worthwhile. My top two sights would be the Temple of Literature and right across the street, the Museum of Fine Arts. The Temple of Literature is amazing architecture and the size of it is impressive. I liked to imagine students of Confusiousism studying while wearing long robes. The Museum of Fine Arts is not all that spectacular in it's entirety but there are two things that I found worth a visit. Some of the Buddhist statues were very unique, at least to me and the lacquer painting from the 1950s are outstanding. I like lacquer because it has a beautiful rich quality to it. These particular paintings combine the traditional painting with contemporary motifs. I believe the contemporary artists in Vietnam shun lacquer, and see it as a thing they do for tourists. They all want to oil paint like the Western artists.
The last place is my favorite cafe. There are hundreds of cafes here in Hanoi, but my personal favorite is at the top of the T of Bang Be and Hang Bac. Staff is not very friendly but not rude either but the coffee is fresh and authentic. None of this instant coffee of the less popular cafes. The juices are watery but the coffee shouldn't be missed. Remember, this is Vietnamese coffee served with sweetened condensed milk.