Getting from the Airport to the City
The easiest way is to use the Metro, located in Terminal 3 (not the underground train station). Get a 3-zoner ticket for 36 DKK from a machine in the baggage hall or by the DSB counter outside or on the platform (you can also queue to be served at the counter). It will be valid for an hour on all forms of transport including buses (show it to the driver as you get on).
Accommodation
For students we have reserved a block of rooms at Cabinn Scandinavia Hotel (Vodroffsvej 55, 1900 Frederiksberg C). It is close to Metro stop 'Forum' and you can walk to NBI in 1/2 hr by the lakeside path (see map) or take Bus 3A from Rosenørns Allé which stops in front of NBI (Irmingersgade).
The lively area of Nørrebro with (cheap) bars, cafes & restaurants is halfway along the route to NBI. The Town Hall Square, Strøget and Tivoli, and the railway station København H are a 15 min walk (or take Bus 2A/250S/66).
Lecturers will stay at Hotel Ibsens (Vendersgade 23, 1363 København) which is close to Metro (and train) stop 'Nørreport'. NBI is a pleasant 20 min walk (see map) or take Bus 6A/42/150S/184/185 from Nørreport and get off near NBI (Rigshospitalet Syd).
Getting to the Niels Bohr Institute
Blegdamsvej 17 is marked on this map. Detailed directions on how to reach the Institute (as well as other useful information) is given here. For metro & bus journeys, you can plan routes here and learn about buying tickets here. For journeys within the city you need a 2-zoner ticket for DKK 24. It is probably not worth buying a City Pass, Flexcard or Copenhagen Card as you will be at NBI all day. You can download 'Mobilbilletter Hovedstaden' from App Store or Google Play and buy tickets on the go (or from the bus driver). Alternatively you can rent a bike.