As an Icelander I have some experience on the matter. I have ridden quite a bit around Reykjavik. I once did the ring road in a 10 man team in a relay race so I actually rode approx 250 km out of the total 1400 km. Here are a few observations from me:
-The roads in Iceland are worse than what one would expect. Rough asphalt. I have ridden in other countries and there the roads are much smoother.
-Expect for near Reykjavik the roads are mostly 2 lanes, 1 for each direction and limited or mostly no shoulder for riding. During the summer there is heavy traffic because of tourists so there is limited room for overtaking.
-Weather can change on a moments notice. Sunny one moment and raining the next. Make sure to bring appropriate and warm clothing.
-There are many hills and steep climbs on the ring road.
-There are some very long stretches on the ring road where there is no food or other service to be had. Make sure to know in advance where you can pit-stop.
-Right now it seems Iceland is a very popular tourist location so accomodation is extremely hard to find. Either book well in advance or sleep in a tent.
-The scenery can be very beautiful so when fighting the headwind remember to enjoy the view
-During july there is daylight 24 hours which means you can ride in the night (although I recommend lights). Some people find it hard to sleep in semi-daylight during the nights so you may want to bring something to cover your eyes.
Finally three useful websites which you might refer to:
http://www.visiticeland.com/things-to-do/activities/cyclinghttp://cyclingiceland.is/https://cyclingtips.com/2015/10/roadtripping-iceland/Hope it helps.