where you can park inside a
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Beetle: Reaching places no one has been before
You can also be fined by parking in not allowed places, but we had no problem and found plenty of free places. For instance, in front of almost all tourist information spots there is free parking, and also beside the Hallgrímskirkja in Reykjavik there are a lot of free spots.
Finally, before allowing you to rent a car, they will tell you to watch this video. You can do it now and save you the waste of time there.