If you're in Hanoi for a short amount of time and want to do a self-guided tour of some of the best local food, then follow this guide to the highlights of Hanoi:
Chả Cá @ Chả Cá Thăng Long
This is one of the best fish dishes I've had in Southeast Asia. It only really exists in Hanoi (you can occassionally find it elsewhere but whenever I've tried it, it's been massively disappointing). Ridiculously succulent fishes of fish in turmeric are heated in a pan on your table along with dill and other vegetables and then served with vermacelli noodles, fish sauce and herbs. It's wonderful and shouldn't be missed, especially if you love fish and dill. It's a bit more expensive that most local dishes (120,000d) but it's worth it.
Bún Chả @ 41 Cửa Đông
This is the most famous Hanoi dish. I've eaten it countless times, including the most popular spots (like Dac Kim), but this local place is the best I've had. I don't think it even has a name but it will be obvious if you go to the address. The portions are massive and the meat is fantastic. Even though the spring rolls aren't quite as good as other places, it's worth ordering one each (or half) as they're great for dipping in to the broth to add some crunch to the dish.
Hủ Tiếu @ Cô Tuân
One of the best noodle dishes I've had in all of Vietnam. Cripsy pork, fresh noodles and a delicious broth. Order a soya milk to go with it (ask for "sữa đậu"). The Bún Bò Nam Bộ is delicious too if you fancy beef instead of pork.
Phở @ Phở 10
This is a great phở at a very popular restaurant so you may have to share a table with strangers. The broth is delicious and the beef is some of the best, but I wish they give you a plate of leaves to add like they do in most of the country.
Bia Hoi is cheap, fresh, draught beer usually sold on the street for about 5,000d. Check out Bia Hoi Corner in the centra of the Old Quarter in the evenings to join in the hundreds of people drinking on the cheap. Unforunately many of the street bars on the cross-roads are now selling more expensive beer but there are still plenty of options if you look around.
The craft beer scene in Hanoi is growing. It's nowhere near the size of Saigon but it's still worth exploring. Standing Bar has a good selection and Hill Station is the perfect place to go between 2pm and 6pm for their 2 for 1 happy hour right in the centre of the Old Quarter.
As with the rest of Vietnam, coffee is an important part of the day. Unlike the south, hot coffee is common. Unfortunately coffee is more expensive in Hanoi than the rest of Vietnam, with most places charging 20k - 30k (literally double the price). Egg coffee (which isn't as weird as it first sounds) is a speciality of Hanoi, most famously at Café Giảng.
And if you have time...
Sốt Vang @ Bánh Mỳ Trâm
French-Vietnamese red wine soup.