Starting from Reykjavik, several daytrips with an ordinary car are possible. The tours I did and will describe were at maximum 350 km long. Tips about driving in Iceland. I didn't see much of Iceland yet, but what I saw was extraordinary beautiful and impressive! It is very barren, but that is what I like. It has been a few years since my last visit, so some things might have changed slightly.

North-West of Reykjavik
Leave Reykjavik in northern direction on road n° 1, via Mosfellsbaer.

Mount Esja : Mountain with snowy tops of 900 m high, visible from Reykjavik.

Hvalfjörður (Whalefjord): Beautiful fjords stretching over 40 km.Clearblue water, rocks, waterfalls a,d mountains. Reykjavik- Hvalfjörður: +- 35 km tot 75 km.

Thyrill : Used to be a whalingstation. There are ugly fueltanks from the NATO who used to have a base here. At Ferstikla road 50 leads into the interior.Reykjavik- Miðsandur: +- 65 km

Reykholtdalur: This a rural area : grasslands with farms.

Reykholt : Historical village at road N°519. Former house of Snorri Sturluson, an important medieval writer. There is an attractive modern church, with an informationcentre and souvenirshop, a few houses and a school/summerhotel. Lively during July and August, in May it was completely deserted, and nothing to see.Reykjavik - Reykholt  +- 120km.

Hraunfossar falls are 25 km further. Water is floating out of  the porous black lavarocks into the river Hvita. This is an extraordinary sight. A little further to the right is the waterfall Barnafoss swirling through the lavarocks. The lightblue water are contrasting well with the black rocks: very beautiful !

Husafell is a favourite spot for Icelanders on vacation.There are bungalows, a campingsite and a small shop with cafeteria. This is a good location if you want to go hiking (or during winter snowscootering) in the environment. You can climb the Strútur (938 m) or the Eiriksjökull.

You can return via Borgarfjördur : a bridge stretching out over 2 km between fjords and the coast.

Other possibilities in this area :

Glymur: A 190 m tall waterfall hidden behind rocks. It's near Thyrill and can be reached via Botnsskáli.

Eldborg : This volcano is 50 m deep and has a diameter of 200 m surrounded by a lava field.

Akranes: A fishing village, but with 5200 residents it is an important 'city' for West Iceland. Of little importance for tourists.

Borg: historical village, with a church built in 1880.

South

Thingvallavatn is with a surface of 84 km² the largest natural lake in Iceland. At some points it is 114m deep. There are several waterfalls. The lake is formed on the spot where there is a crack in the earthcrust caused by the drifting of the continents Eurasia and America.Situated near Thingvellir. 

Thingvellir : National park extended over 50 km² of great historical importance. The first parliament of Iceland   (Althing) was established here in 930 AD.  The members of parliament gathered   in the open air to listen to the law which was recited while standing on the 'lögberg' ( the Law Rock). These meetings were followed by celebrations.

Haukadalur / Geysir : Geysers and boiling soil.

Gullfoss : very beautiful waterfall.

Stöng : ancient farmhouse.

Reykjanes

I found this a very nice part of Iceland : it is very barren with a dark soil and it looks like you're on the moon.

Bessastadir : Official residence of the president with a small 18th century church. Beautiful view on Reykjavik.

Hafnarfjördur : Fishing village with fishery museum and postal museum.

Hafnir : Tiny village with a nice small black wooden church and an aquarium.

Kleifarvatn, Krisuvik : Green lake and active hot wells.

Bláa Lonid or The Blue Lagoon. Very popular attraction. Geothermal station and open-air swimmingpool heated by the heat of the soil. Everyone loves it, but I found it was like swimming next to a factory. The geothermal station is ugly, but the water feels great and it should be very healthy.

Reykjanesta, Reykjanesvista: At the tip of the peninsula. A lighthouse and an impressive view on the 'bird rock' and on the 'bird island' Eldey. Very beautiful !

Gunnuhuer : Green lake and sulphur wells: the earth boils here. Great to look at, but it smells terribly.

Reykjavik

Reykjavik is a small, but nice town. For more information on the city, please visit one of the following links.

Toeristische dienst van IJsland :  http://www.icetourist.is/
Uitgebreide informatie : http://www.travelnet.is/
Allerlei nuttige adressen : http://www.glacier.is/tenglar.htm
Activiteitenkalender : http://www.whatson.is/
Officiële site van Reykjavik : www.tourist.reykjavik.is