Bern
 

What is the nearest airport to Bern? We will be in London for 2 weeks and are considering a 2 day break to Bern.

Bern has its own airport, but you might also cosider Geneva which is a couple of hours by train (If I remember well) from Bern.
Bern is nice and a 2 day break is the ideal. It has the longest shopping covered street (with arcades) in the world (if I am not wrong), the city centre is simply lovely and I suggest also to go to the GURTEN, which is a little mountain just outside Bern. I think you must take the tramway 1 and then take a small train that goes along the slope of the mountain. You will enjoy a beautiful view on the whole city. Lot of green, trees, silence... nice! Near the Hauptbanhof there is a tourist information office for any other info.

Zurich is another close major airport. In fact, when we landed at Zurich, we took a train directly from the airport to Bern and arrived by mid-morning.

There are not a lot of flights into Bern and few if any non-stop flights, so with only 2 days, you might want to look into flying into Geneva or Zurich as mentioned above. It also might be cheaper to fly into Geneva or Zurich. One problem with Bern airport is that there is no train station, so you have to take a bus from the airport to town, and I think they only run once an hour. A taxi would cost you almost as much as train fare from Geneva or Zurich.

The train from Geneva to Bern takes 2 hours and is a very pretty journey, as you ride the ridge high above Lac Leman. Round trip fare is CH 95. Many trains are direct from the airport, i.e. don't require you to change trains.

The train from Zurich takes 1.5 hours. It is not as pretty as the ride from Geneva, IMO, no real vistas. Round trip fare is 87. Many trains are direct from the airport, i.e. don't require you to change trains.

Take a look at rail.ch for timetables. You want trains from Geneva airport or Zurich airport.

If what cicerone says is all ok, Bern airport has also its advantages.
The shuttle service to the trainstation in Bern is ok.
The great advantage of Belp (which is the name of the airport) is that check-in time is reduced to a minimum. 1 hour to 30 minutes before departure is ok.
It also is an airport you can't get lost in!
Check on flights from London City airport to Bern.

If you want to do extensive taxfree shopping, as you are going outside the European union, forget Bern and take... Geneva, for the vistas on the train trip.

Thanks for all of the quick replies. My great grandmother was born in Bern so I'm going for genealogy info, not for shopping. But if some shops happen to be nearby, well....