If you're in Reykjavik, you can get a Reykjavik city card. This card (valid for 24, 48, or 72 hours) includes use of the city buses and free (or discounted) access to many of the sights. You can buy the card at the shop in the lobby of the Hilton Nordica.
Link:
https://visitreykjavik.is/city-card/where-to-buy