There are many parking zones in Reykjavik, multi-level car parks, lots, and street parking that are divided into 4 zones (P1 - red, P2 -blue, P3 - green, P4 - orange) with the closest zone, P1, being the most expensive. Parking is free on Sundays. Also, if you're outside of the P1-P4 zones, you are free to park anywhere.