Bun cha (supposedly) originated in Hanoi, so what better place to get it than in Hanoi.
Bun Cha Dac Kim is one of the most famous spots for bun cha (grilled pork with noodles) and for good reason.
Make sure you got hungry because it's a lot of food. For VND90,000 (as of April 2016) you will get the noodles, vegetables, grilled pork, and two egg rolls. The servers, while not all that warm, will show foreigners how to eat it--mix some of the chili peppers and garlic into your bowl of grilled pork, take some of the noodles and mix it into the bowl with the pickled vegetables, get some lettuce and basil, put some egg roll in the pork mixture, and eat all together.
There is an English menu, but really it seems like the servers will bring you the bun cha without ordering.
In terms of cleanliness, like in a lot of Southeast Asia, try to turn a blind eye. The greens on the table are recycled, meaning they get left there for the next person. Just pretend you don't realize that and enjoy the food.