Reykjavík is not particularly pedestrian-friendly beyond the downtown area (aka 101). Most Icelanders get around by car, and though there is a bus system, it isn’t terribly extensive. For this reason, a one-day walking tour of the city is best experienced within the 101 area, where you can get a little bit of nature and have a whole lot of fun without needing to decipher bus routes or having to hitchhike.
Reykjavík is an eclectic, colorful city with a downtown area that is the perfect size for a walking tour; you’ll be able to see everything that you’d want to in just a day.