Reykjavik has sidewalks next to practically every street so walking in Reykjavik is easy for people who feel so inclined.
The maximum speed limit in Iceland is 90km per hour. In urban areas, the limit is 50km per hour but once you are out on the open road it’s 90km on paved roads but 80km on gravel roads. No matter what the speed limit is it’s very important that you adjust your speed to the driving conditions.
When driving in Iceland you are likely to encounter difficult gravel roads, sudden icing on roads, animals, single-lane bridges, and otherwise tricky roads to drive. Also, roundabouts work differently in Iceland from many other countries, regarding right-of-way.
Further information on driving in Iceland is available here and guidelines about getting a driving license are available here.
Reykjavik is cycle-friendly now that the city has designated cycling routes and cycling is becoming increasingly more popular. Cycling in the summer is nice and easy and getting snow tires makes cycling in the winter both safer and easier. It’s normal to cycle on sidewalks instead of the road but please note that pedestrians have the right of way. Reykjavik and its vicinity have many mountain biking trails for those looking for more action.
Reykjavik buses are called Stræto. Prices and schedule information can be found on their website, https://www.straeto.is/en. There is also a really good app called Straeto (make sure you add the app with the big yellow logo) which allows you to plan routes, see the exact current location of the bus you want to catch, and buy individual fares.
As of March 2021, bus passes are purchased through an app called Klappið. Registration and app links can be found here https://www.klappid.is/en.