Explore all that Reykjavík has to offer on your own. Walking Laugavegur and Skolavordustigur is a great way to capture the essence of Reykjavk, both are amazing shopping streets. Browse in shops, often the tiniest places sell the more unusual items, relax in a charming caf then wander some more. You will come across local crafts, the iconic tall white Hallgrmskirkja church, its design is inspired by Svartifoss waterfall at Skaftafell. For a grandstand view over the city go to the top of the tower, it is well worth it!
There are a few fabulous museums, covering everything from history and the building of the Icelandic nation at the National Museum to photography at the Reyjavk Museum of Photography, or Icelandic culture at the Culture House. If you love art, there are quite a few galleries including the National Gallery of Iceland, Reykjavk Art Museum and Kjarvalstadir.
Rekjavks thermal swimming pools are open early and into the evening. The largest open air pool, Laugardalslaug, has great hot tubs where you can relax with the locals and tourists. All year round outdoor bathing is very big in Iceland! There are a few other pools close to the city center, all have hot tubs.
Your comfortable hotel or guest house will be within easy reach of the attractions in the city. All districts are served by a regular bus service to the city center. Local buses are operated by Straeto, timetables and information in English can be found here: https://www.straeto.is/More ideas for making the most a short time in Reykjavk, including money saving tips, can be found here: https://adventures.is/blog/top-things-to-do-in-reykjavik-in-2-days/, more information about things to do is available here: https://adventures.is/iceland/locations/reykjavik/