There are plenty of walking / hiking possibilities but there is not too much information easily available in English. One problem is that there are not that many well marked paths / trails.

The following links may help:

For an overview www.bugbog.com/walking_tours/iceland.html

Some links in and around the Reykjavík area visitreykjavik.is/desktopdefault.aspx/…

Customised tours - it might be worth calling / emailing on the off-chance that they have something happening which you could join http://www.isafoldtravel.is/edefault.asp

For reasonable accommodation at short notice it's always worth checking the Farm Holiday Service http://www.farmholidays.is/ If you also use the Icelandic site http://www.sveit.is you'll find phone numbers listed - identify your selected farm using the English site and then use the farm reference number to look up the same farm on the Icelandic site, and call the farm direct for a last-minute booking.