The race start is in the east part of Reykjavik. To get there you have several options:
Jog, bicycle or drive. From the city centre it´s only a 6,7 km drive to the Race Start. See map here.
Taxi from city centre will cost approx. 4000 for 4 pers. and 5000 for 5-8 pers. The address of the race start is Rafstöðvarvegur 4, 110 Reykjavík, see map
For more information about the main taxi company in Iceland is Hreyfill.
Busses no. 3, 11, 12 and 17 stop close to the start. The places to hop off are Vikin (800m walk to the start) or Blesugrof (900m walk to the start) see map. You can pay in the bus. Single fare is 460 kr. ($3,5) and they don´t give change.
More information about the busses in Reykjavik: here – Saturday schedule.
For the marathon runners the busses are not an option. The race starts to early.
A good map of Reykjavik and main towns in Iceland: here