The brilliance of Hanoi is that your high budget doesn't get you better food. There are great posts on CH about Hanoi street food, and I've just recently left Hanoi and only ate in a restaurant once (and it was my worst meal). It was delicious and safe. Spend your money and hire Hidden Hanoi to take you on a food tour of the markets and the Hanoi food culture. Take one of their cooking classes if you have time and then eat on the street! A few standouts are:
Pho 10- 10 Ly Quoc Su
Bun Cha Dac Kim (lunch)- 1 Hang Menh
Bun Bo Nam Bo (67 Hang Dieu)
In terms of great restaurants, Anh who runs Hidden Hanoi recommended Au Lac house.