If you're going in Skaftafell and the weather is good, I'' definitely say the walk. You'll have an amazing view on 2 glacier tongue at the same time.

If you have to choose something close to Reykjavik, I would defenitely go to Hveragerdi, It's an hour drive from r'vik and when you walk North- east though the small town, a very nice walkingtrail will appear. The first part is called reykjadalur. You walk along a warm creek and you can even bathe in it. There's a hut where you can stay, as long as you take your own gear with you. I like this trail very much as it's quiet, it's quite green, but there are loads of fumaroles and stuff as well and because of the bathing ofcourse!

Landmanaulgar or Hekla.. There are nice places around Thingvellir (north from the park, up the mountains.. no people, silence, perfect place to rest)

If you're kind of fit, you can do the Fimmvörduháls-trail in one day. It takes you from Skogar to Thorsmörk in about 8 hours I think. You can stay at Básar Campsite and Hut (www.utivist.is) and take the bus back the other day. Thorsmörk is generally good for day tours, too. Depending a bit on what the Krossá river plain looks like, you can get to several glaciers and river canyons.

my insider tip:in order to really feel like in the middle of nowhere(not so difficult when u get out of Rejkjavik:-) is a hiking in Landmanaulgar. A bit difficult to reach but absolutely awesome, impressive rocky hils in different colours and some hot pots to relax in the evening:)))

In Reykjavík, people climb Esjan all the time. It's relatively easy, close by and you can be up and down in a couple of hours. You can even get there by city bus from the centre!

Also there is this Icelandic adventure and activity company with an emphasis on eco tourism and environmentally friendly trips in the amazing Icelandic nature. They offer many types of Hiking and Glacial Hiking and also lot more like Rafting and snorkeling and many more... You can check out their hompage: www.adventures.is

Þórdís is right, anywhere can be good as long as you have good boots and common sense! "fi.is-> á slóðum ferðafélagsins" and "ganga.is" have some suggestions, of course in Icelandic but maybe enough to get ideas, "1 klst" is one hour, the map at ganga.is is pretty good

the Mt Hengill area is a very good place. you can find a map and choose the length of your hike. you can go hiking almost anywhere in iceland and tourist centers have really good maps and the information you need.