I adore Iceland, went for the first time this year in March having heard a lot about it from friends that work there and I really want to go back, the wildlife and landscapes are incredible (so amazing they even tempted me into trying my hand at landscape pics!)
We definately went the route less travelled and headed to the Snaefellsness peninsular, mainly because I wanted to catch the orca that hunt there at that time of the year. We barely saw anyone, was almost spooky! We did drive as far as Vik on the south coast in the end but soon headed back to Snaefellsness as it just knocked the socks off everywhere else for us, the landscapes are stunning almost where ever you go but there were no crowds, barely any people really and all the locals there were so friendly.
We did not hire a 4x4 and stayed in hostels. We were fine with the car despite a lot of snow/ice in the mountains, a few white knuckle moments going over the snaefellsness pass (nervous probably due to our inexperience driving in snow than any real risk!) but we didn't try anything silly so didn't get stuck.
That time of year you can beat the crowds even at popular places like the geysirs (to see strokkur errupt). We got there as soon as the park opened and got the geysir to ourselves for half an hour! Was extremely cold though XD