In Iceland so far is legal to park and stay overnight anywhere, at least at the moment :). But in the city even this possible I recommend you go to go to the campsite or http://www.reykjavikcampsite.is or find some quiet location out of the city center:
- around the Esja mountain
- around the lake Reynisvatn
- around Hraunahverfi in Hafnarfjörður
- Grótta lighthouse parking
Wherever you decide to park and sleep please be careful with the environment.