Any suggestions for reasonable lodging in Reykjavik?
1)Try a B & B or room in a house in lieu of a hotel, 2) try booking.com and look up Hotel Fron among others, 3) consider the hostel in the center of town - it's clean, well located and probably more affordable than other places. It's very easy and safe to get around in Reykjavik, so you should be open to staying a little on the periphery as well (if you need to)
I don't know if you're still looking but I found a reasonable one - Loki 101 Guesthouse - for about $125/day. Includes breakfast too. Check it out on the Internet. It's conveniently near the Hallgrimskirka (the tallest structure in Reykjavik)