This is a "copy and paste" of my own reply to another RS Forum question concerning accommodations in Reykjavik.
There are many options, there, but we were pleased with the one we selected.
Typically, guesthouses have "shared facilities" - and this one is no exception. However, there was no issue at all during our stay. Our room was quite large, the lavatory was very nice - we were on the ground floor - and the simple continental breakfast was an added plus. It is not inexpensive, though. Almost nothing in Iceland is inexpensive.
In July of 2017, we stayed at the Freyja Guesthouse, located very near the giant steeple church Hallgrímskirkja, Free parking was included as was breakfast and use of bicycles. Nice area. I would stay there, again. Here's a link....
https://www.freyjaguesthouse.com/