The very notion of "cheap car rental" in Hanoi is meaningless: there are huge taxes on cars.
That's why car rentals in Hanoi are priced solidly, and you'll find many more moped and bicycle rentals.
But even if you find a car rental in Hanoi, you can't use a car around the clock: personal use is only legally allowed during certain hours, otherwise the whole city would be one big traffic jam.
You might want to ride a moped, which you can rent from most hotels in the city? It's more convenient and cheaper than an auto. In Hanoi, renting a moped will cost about VND210,000 per day plus gasoline costs.
If you're determined to rent a car in Hanoi without a deposit, you can do so right at the airport. It is possible to rent a car with or without a driver. You can also rent a car by contacting Thanh Hung Group (104-106 Nguyen Van Cu, tel: (043) 8-213-213).
The rental cost depends on the type of car and the rental period and starts from VND500,000 per day.