Reykjavik is a very cool place and if you choose your accommodation (and attire) properly is pretty easy to get around by foot, or bike. I always pack some good shoes and this was a great city for walking around! Excellent paths along the shore and up to the Pearl, and easy walking around Reykjavik 101 and the shopping streets.
For those of you who are not familiar with Icelandic streetnames and their location (and that includes myself!), I've pasted in a map of Reykjavík city centre. It might take a second to upload. The city centre is small and very walkeable.
The best way to go around Reykjavik is to stay near the city centre and go around on foot. The city centre itself is not too big - walking from one end to the other will only take 15 min.
Bus transport is expensive and best way is just to go on foot.
Reykjavík main center isnt that big, actually its rather small, probably like justa quartier if you live such ina big city like Barcelona, london , Paris etc.so its easy to go walking everywhere, its easy to walk around cause almost every single street in the centre is connected to the main street Lauvavegur. Take a map and walk around!
Actually we walked rather than took any public transportation. If not for the cold weather, Reykjavik is a great city to walk in.