Budget

Ha Noi Xua
If you want to eat traditional dishes from Ha Noi, from 100% Hanoian, you can try this restaurant. The owner used to live in Czech republic and Germany before moving back to Vietnam. In the morning you can have a tasty bowl of Pho and for lunch Bun Cha or Bun Nem, really tasty and maybe better than in Ha Noi. Open til selling out the food (about 1PM). You can find it at 95A Nguyen Chi Thanh.
Quán Huế Ngon
Slatted wooden tables and chairs tumble out of this little restaurant on to the pavement and are filled with locals on an evening. A variety of traditional Vietnamese hot-pot and barbecue are available, cooked at the table. Friendly and helpful staff speak Vietnamese, while the manager speaks some English. A picture menu is available with descriptions in English. Very good value. 65 Trần Quốc Toản Street.
Tams Pub and Surf Shop
A great place to rent surfboards even though the waves don't get really big till the winter swells pick up and even then they do not get all that big. GIs during the Vietnam war used to surf here and in this restaurant you can see the stories unfold with pictures on the wall. The pub and surf shop is ran by Tam and her family who boast the best burgers in Vietnam. I would go as far to say the best burgers in all of Asia but I have not been to all of Asia.
Hoa's Guesthouse at China Beach
The gathering spot for backpackers in the evenings, as Hoa hosts "family dinners." For about US$1.50 you get treated to an all-you-can-eat buffet, courtesy of Hoa's wife. Picnic tables are full of travellers inside this tiny cafe, starting at around 7PM. Closed during Tet.
There is a food court on the 3rd floor of Indochina Riverside Towers, 74 Bach Dang. There are about 10 stalls to choose your meals and drinks, Vietnamese, Korean, Japanese, and Chinese. Great river view and free toilet too. It's the same building with HSBC on the eastern side of river Han.