In Hanoi now, wanting to avoid the airport taxis we went for the local bus option (down to the left as you exit the airport) we wanted to catch the #7 or #17 which take you to bus stations in the old quarter (for around 30 cents USD), so did many other tourists (all standing around going "do you know where the #17 bus is") but none of us had much luck in trying to convey our message to the Vietnamese people so we ended up on what I understand was a Vietnam Airlines bus for 30000VND. This took us into the old quarter and I'm not sure of its final destination but we got off and got a taxi (a good one luckily) to the bus to Cat Ba, it was all quite easy and successful, I think the main aim is just to make it into the city. On returning from Cat Ba we got ripped off with the bus station touts (the meter runs normally at first but is rigged to jump up) we knew it had to happen eventually, but as soon as we saw the meter jump (they angle it up into the sun to make it hard too see) we told him to pull over and just jumped out and got another cab for a decent fare (metered). We have since been told by our hotel and eating establishments that the trusted taxi companies in Hanoi are Hanoi Tourist, Hanoi Taxi, CP Taxi and MaiLing Taxi. So far we have found this to be true. We have got our hotel to order us a car back to the airport (flight leaves before bus station is open) and this will cost $15USD which is apparently the new going rate. Hope this helps someone to not get ripped off!!!
Just to add a little to that useful email:
The Vietnam Airlines bus usually drops off at their office on Quang Trung, which is just to the South West of Hoan Kiem Lake. You can also pick it up from here to get to the airport.
There are also private minibuses which drop off somewhere central - they should also cost no more than 30,000 but can be overcrowded.
Another alternative is the Jetstar bus which is more comfortable than the minibuses operated by Vietnam Airlines and a similar price. Last time I passed through the airport I was pounced on by Jetstar employees selling bus tickets and it was all above board and easy.
$15 is the going rate for a taxi from Noi Bai to Hoan Kiem (go to the official taxi rank don't just go with someone who grabs you inside the terminal) although if you're booking from town to the airport you should be able to get it for a bit less by booking through one of the travel agents in town.
The #7 bus doesn't go into the Old Quarter but stops about 4km away - however, I live near its route and haven't seen one so I'm not surprised you had trouble finding it at the airport!