You should stay in Reykjavik for at least 3-4 days, because that is how long it will take you to see the sights in and around the city. You could then take an 3-4 day trip to the interior Highlands and the south coast.

Tours run the, 'Golden Circle' route, which is described in most guide books. This includes visiting the Kerið volcanic crater, Gullfoss waterfall, Geysir geothermal area, and Þingvellir Natnl Park. This is all a do-able drive in one day.

On another day, you can drive the South Shore, from Reykjavik to Vik, stopping at Seljalandsfoss and waterfalls, the Mýrdalsjökull glacier (consider a snowmobile tour), and the beaches near Vik. By then, the shorebirds ought to be arriving. This is a day-trip, but you could do it overnight if you continue along the coast, or take the ferry over to the Westmann Islands, where there are tons of birds and active volcanic features.

You could also take a 'superjeep' tour of the interior highlands - you can't do this yourself, but you can drive to the location where the tour leaves.

Another nice drive is through the fishing towns and coastal areas of the Reykjanes Peninsula. Along the way you can stop at the Blue Lagoon Spa and geothermal power plant.

Here are some of the phots that I took on our last trip:
http://mysite.verizon.net/res1dm2h/index_2.html

We just got back from 4 days in Iceland. We followed the advice of this forum and and guidebooks and made Reykjavik our base with day trips out. My viewpoint will not be popular, but if I had to do it over again I would not have done that. I, too, am an amateur photographer plus a hiker and using Reykjavik as a base is limiting and extends your day trips by a minimum of 2 hours each day. Reykjavik is a very nice city, very European, but considering my limited time not particularly spectacular and other areas of Iceland are absolutely spectacular. If I had to do it over again I would skip the Golden Circle. I felt like that is a marketing gimic since it can be accomplished in a day, but I have seen similar sites in other places. I did feel the waterfall at Gullfoss was definitely worth the stop, but if you have seen other geysers, I would avoid Geysir and if you are not with a tourguide who can provide info, I would skip the other stop (the historical stop).

I suggest two to 3 days driving along the south coast. Just before Skogar it becomes spectacular. The folk museum there is worth the stop as is the bird viewing areas before Vik. Definitely stop in Vik and walk west along the beach to the caves, etc. Vik looked like a good place to stop for a night. Things we did not have time for because we made Reykjavik our base and drove the Golden Circle is driving east from Vik. I understand it gets better and better and I'm telling you Skogar and east was spectacular. I also wished we had time to drive out Route 26 to get a closer look at Helsa. It also sounds like the west coast is a very beautiful drive with lots of photo ops. I also found out you can do a day trip to Greenland - it is a two hour flight each way. The other recommendation is to take a flight from Reykjavik to the large city in the north (can't remember it's name) and spend a day or two driving up there. Iceland is an incredible place. Don't get me wrong, Reykjavik is a nice city, but when you have limited time and goals which are not tied to the city, I think venturing out and spending the night wherever is a good idea. The tourist board has guides of places to stay on farms, b&bs, and guesthouses. That kind of info plus a really good driving map and a ton of film, plus spare batteries, is probably all that is needed. Enjoy!!!

To Katrinasl:

Thank you so much for your excellent comments regarding tours of Iceland.
Could you offer advice for us who have only one day in Iceland? We arrive at 6:30 in the am and leave the next day at noon. We don't mind hiring a private guide. We would like to see as much as possible. As you can see, since we have elected for one day, we need an overview. Thanks so much.

If there are a number of you (at least 4) it would be cost-effective to hire a private guide, who will take you around to more places in a limited time. In another post, I mentioned an extraordinary guide that we hired, Oli Schramm, who runs Highlander Adventures (www.highlander.is). In a day-and-a-half, he (or someone like him) could put together a nice overview of Reykjavik, Geyser, Gulfoss, Þingvellir, Reykjanes Peninsula, and Blue Lagoon.