Here’s a brief guide to the remaining districts from Wikitravel:
Hai Ba Trung District: “Located south of Hoan Kiem with the largest population of all districts. Its northern part also has French-style streets with big trees. A large number of universities, including the Hanoi University of Technology are located here. Times City, in the southeast of the district, is a huge shopping mall with an aquarium located within the complex.”
Dong Da District: “One of the original four central districts, is mostly residential. The Temple of Literature -- Imperial Academy (Van Mieu - Quoc Tu Giam), Vietnam's first university, is located in the north end of the district, bordering Ba Dinh.”
Cau Giay District: “Houses a large number of universities, including the National University's main campus and Hanoi University of Education. The Museum of Ethnology, one of foreign travelers' favorite, is located in this district. Its southwestern part bordering Nam Tu Liem district has numerous high-rises, including Keangnam Hanoi Landmark Tower, Vietnam's tallest building. This is where you see a completely different side of a modern Hanoi, in contrast to the old inner districts.”
Long Bien District: “The only urban district located east of the Red River, it is named after the iconic Long Bien Bridge. The Bat Trang ceramic village and Le Mat snake village are located here.”
Thanh Xuan District: “Houses Royal City, Asia's largest underground mall. Inside this mall, there are an ice-skating rink and a water park. The plaza above ground have large, cheesy looking Greek god statues.”