Getting from the airport to the city centre
The easiest way to get from the airport to the city centre is to use the Metro, located in terminal 3, past the entrance to the trains. You can buy a ticket on the ground floor level at the vending machines or at the desk after exiting the baggage claim hall. You will need a 3-zone ticket, which costs DKK 36.00.
Getting to the Niels Bohr Institute
The Niels Bohr Institute at Blegdamsvej 17 can be found on this map. If you want to take a bus from the hotel to the institute you may need a 2-zone ticket, which can be purchased from the bus driver for 24 DKK (make sure to have coins). Alternately, at most metro and S-tog stations you can buy a City Pass Small (1-4 zones and covers also the trip from the airport to the City of Copenhagen) and City Pass Large (covers the entire metropolitan area). The card comes in four versions: 24, 48, 72 and 120 hrs, see here.
For S-tog (eg. light train or S-bahn), metro, and bus journeys, Rejseplanen can be used to find routes.
For more complete information on transportation in Copenhagen including ticket options see the official city tourism site VisitCopenhagen.com.
By far the best way to get around Copehagen is by bicycle. These can be rented from bicycle shops or your hotel might have bicycles available for guests. There is a bicycle share system, but at the current time it has too few stations to be really useful.