We have done three tours in Iceland, an absolutely amazing place to tour. Can concur with heatonrider that the ring road is best avoided particularly in the south and south west as it is very busy in the summer.
The cycling in the interior is amazing for the scenery but can be hard work on some of the gravel roads due to the washboard surface that can be created by the 4x4's.
To help you here is perhaps our top places that we enjoyed and worth visiting in no particular order.
Myvatn - lovely lake in the north with hot springs, the Krafla eruption lava fields, Dimmuborqir, psuedocraters at Skútusaðir and the Hverfjall volcanic crater.
Jökulsárion - Glacial lake with icebergs floating in it.
Látraburg - sea cliff with Puffins & Kittiwakes.
þingvellir - a rift valley and Iceland's parliament.
Geysir and Gulfoss
Western fjords
Langmannalaugar - hot spring area and wonderful scenery
Kerlingarfjöll - hot spring area and wonderful mountain scenery.
Snaefellnes peninsular - south side beautiful and serene area with wonderful bird life.
Some of these are in the interior and would require going on the gravel roads. You can see more details and information on
Iceland here and from
our travelogues.
Remember you can use buses to get you to places as they will all take bikes. There is even a bus that goes up and down the 35 on the Kjölur route and in to Langmannalaugar.
There are some routes that you can take to avoid parts of the ring road. To avoid the Keflavik to Reykjavik and Hveragerði you can go via Grunavik. It was gravel road when we did it 2008 but it is now tarmac.
The Reykjavik to Baula bit can be busy and you can't go under the tunnel at the Hvalfjordur fjord so you have to go all the way around the fjord so you could instead go up to þingvellir and then take the 550 over the Kaldidalur route to Husafell and then on to Baula. It is a rough gravel road but there are no rivers to fjord and it is very scenic.
Hope that helps.