I have not been to Iceland (yet!) but from reports of a few people I know who have, if you are in a group the best thing to do is to hire a car and split costs between the group. The roads that go around the island are apparently in good condition from what I have heard, but once you start trying to head into the centre of the island, things start to get less maintained.
By yourself, it is probably cheapest to do some organized tours of some description I would guess. about 10 years ago
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hitch hike. (the hitch hiker is there so you can do your good deed for the day. max)
bicycle, one of the best places to ride, as one can ride around the whole country.
so combine them.
hitch hike with a bike. (an ultimate way of travel. max. )get a ride in a truck or caravan or trailer, between the places you want to go then you have the bike to explore that area.
two individual travellers hired a car together, via the contacts via couchsurfing.org , (discount price) and went mountain climbing in the middle of the night still in daylight.
went Reukjavik- to north east peninsular, road 1-tunnel-51-54-mt snaefellsjokull-56-54-back. 4days. then golden triangle extended to the open geothermal area somewhere around selfoss. the person with me then had never been in geothermal area and i was able to let her explore a whole land scape of open mud pools, steam vents,live craters, rainbow colours. that she found far better than the geysir area and all the tourists.
and go the the gap, where the east and the west tonic plats meet and have a foot in each world up the very top end of the valley. about 8 years ago