since it's Iceland day on the bus ride again and I happen to have been to the country a few times, although not nearly as frequently and extensively as I would want, here's a few pointers for everyone who might want to check out the sights with their own eyes:
Iceland is worth every minute if you can get the chance. My hint - fly Icelandair in Economy Comfort class - the extra space is worth the moderate surcharge and it's quite comfortable. You'll get there and come back quite relaxed. Their standard Economy seats are not great at all and check-in on your flight out of Iceland is a disaster in Economy - if you want to fly Eco class, choose Iceland Express, lower fares and at least equal seats with a much better check-in. Do NOT fly any non-Icelandic airline into Iceland - I know what I'm talking about
Renting a car is also my recommendation - you'll get almost 3 days of rental of a small vehicle for the cost of the cab ride airport-Reykjavik and back. (if you don't want to get a car, use a transfer bus, but you'll then be subject to tourist herding on everything you visit. Not ideal.) When you drive, mind those speed limits (90 kph/55 mph on paved roads, 80 kph/50 mph on gravel). You don't want to go faster in that kind of landscape anyway - you'll only miss sights. If your speedometer is more than 5 kph over the limit, slow down and start enjoying the place!
If you go the Golden Circle - a must regardless of how you do it - on your own, do it COUNTERCLOCKWISE. The tourist buses all do it clockwise, but the real treasure is driving the 365 towards Thingvellir in the evening, when the sun is almost setting, seeing that lake like molten gold. You never get that with a bus. Besides, the buses just don't give the "but I want to stop here and take in the landscape" service.
By the way - Blue Lagoon is somewhat a tourist trap. Don't pay the quite high entrance fee unless you plan to make extensive use of the spa and sauna - 5 hours minimum. Instead, just pay 350 crowns ($4 / €3) to get into one of the Reykjavik municipal pools and enjoy the steam baths and hot basins at your leisure. For winter travelers, enjoying an outdoor pool at 28°F /-3°C is something you can really only get in Iceland. Do it
If you want to enjoy the right soundtrack while exploring Iceland on your own - any romantic composers or John Williams soundtracks will do quite well although very little will beat the powerful sounds of Mahler symphonies if you like that kind of music which seems to be made for this country and its rough and primal beauty.
Restaurants in Reykjavik can be quite expensive although universally serving great fare. If you're into fine dining, Perlan is a must (dress at business casual to lower semi-formal level - no need for black tie here) with a cuisine at upper one star level. Reservations are strongly recommended and plan about €70 / $100 per person including wine and an after-dinner spirit (the local Brennivin is for the courageous and spirit-wise only. Those who don't enjoy a rough, intense spirit should pass). If you have a group of 8+ people, try to take your after-dinner drink on the quite hidden upper level of the 6th floor bar. It's a rather unique place. If you're rather interested in a cheap but healthy dinner, go to a 1011 store (open 24 hours) and fill a bowl or two from their excellent salad buffet and eat it in your hotel room - an unusual but quite satisfying and excellent quality dinner for less than €15 / $22. An Icelandic beer is recommended with this one if you drink alcohol at all - it's low alcohol (3%) and tastes quite good. If you don't drink alcohol, get one of their excellent mineral waters. They're all good. Fast food is almost nonexistent in Iceland after both McDonald's and Pizza Hut have closed. A few Burger Kings remain, but they are in awkward locations.
Iceland is not a country for shopping unless you want to stock up on some local clothing or Icelandic music. 66° North makes excellent but not too cheap winter clothes that will last you for many years, but that's as far as fashion shopping in Iceland goes.
Good luck and enjoy Iceland. You can go pretty much any time of the year although April to September is recommended. Dec to Feb visits are for experienced travelers only although they can be highly rewarding - you want your first glimpse of the country in the warm months.