Drive along Road Nr.41 into Reykjavik and then follow the road signs to the city center.
Drive under three bridges and travel through 3 sets of traffic lights, when you pass the third bridge you will see the Hotel Nordica on your right.
Alternatively you can take a Taxi or use the Airport bus service.
The shuttle service bus goes from the hotel to downtown Reykjavik and the botanical garden is within 5 minutes walking distance.