I’ve been twice now, in 2005 and last summer.
I have never cycled there but I think the best way to see the wilderness (if that’s what you’re after…) is to hike the laugavegur and fimvorduhals trails. Seriously amazing scenery, a challenge and mountain huts en route if you’re not up to camping in snow storms…
On my last trip there we bumped into an American bike packer and we met him each night at the designated camp spots (it’s protected national park, so wild camping is strictly forbidden). Anyway, he said he ended up pushing most of the trail. After all, it’s mostly snow, ice, river crossings, ash deserts and big, steep, unforgiving ascents.
Can’t recommend Iceland enough. I want to go back already!
The food is good, although avoid the putrid shark (an Icelandic delicacy) and the people are very hospitable.
Reykjavik has a great nig life as well.