Depending on how much time you have, start from Hoan Kiem Lake in the old quarter, which is a big and well-maintained lake. It is very pleasant in the evenings, and you can pick a spot to do some people-watching in Hanoi.
The other lakes that you can visit are Lake Truc Bac and the West Lake.
Getting around in Hanoi
Hanoi is easy and comfortable for traveling around, with numerous options to explore the city. The local bus system is very good and cheap to use, if you figure out the routes and maps (some names are in Vietnamese, so you'll have to refer the map routes of the buses to use them).
Rent a motor bike if you know to ride one, because this is a great way to explore Hanoi. You can go where you want and even venture farther if you have time along with the fuel prices being cheap.
Most attractions are in and around the old quarters. So walking would also be a great way to check out Hanoi. For specific places, make use of local taxis, tricycle or mopeds that are cheaper too.
Where to stay?
The old town of Hanoi is where you should stay while in the capital, hands down. Not only there are excellent accommodation options for all budget ranges, you'll have a chance to taste the local Vietnamese cuisine in the plenty of restaurants and eateries.
So that's how I spent my 2 days in Hanoi. I also explored a little more on my own apart from these attractions as well. But these are what you shouldn't miss while in Hanoi!