On the west end of Reykjavik is a peninsula bearing the name Seltjarnarnes. It is easy to circle the peninsula in few hours and on a bright day you are in for a treat. From the northern shore you will see the mountain Esja in all its glory and all the way to Akranes over the Faxafloi bay.
At the northernmost end you can walk during low tide to the iconic lighthouse Grotta, but you better be back before the high tide. On the southern shore you will enjoy a view of the Reykjanes Peninsula and its beautiful mountains.
Decades ago the road along the shore in Reykjavik that leads to Seltjarnarnes peninsula was called the Love Lane. It was common to drive there at evenings to watch the spectacular evening sun in the summer and perhaps dreaming of the future with the one you love.
Anyhow, you can walk this road instead of driving it as there is now a walking path all the way from Reykjavik center to the Seltjarnarnes peninsula.
Here is a trailer originally for a movie that catches beautiful moments at Seltjarnarnes.