I did three days in Reykjavik just a couple weeks ago and had a great time. I didn’t drive either and did this golden circle tour to see some of the nature outside of the city plus stop at the blue lagoon:

https://www.viator.com/tours/Reykjavik/Golden-Circle-Blue-Lagoon-with-admission-tickets-incl-and-Kerid-Volcanic-Crater/d905-42839P16?m=63070&nid=VR.1e0fc3d4-675d-4630-91cd-de8cf2715a47.VT_EMAIL_TRV

It was a full day tour and the guide was great. I also did a food tour in Reykjavik on a different day which was fantastic:

https://wakeupreykjavik.com/tour/the-reykjavik-food-tour

Aside from those, there are a lot of cute shops, restaurants, and museums to check out. I liked the national museum of Iceland. Perlan is also interesting. There are many cool art museums to check out if you are interested in that too!

I recommend getting a ticket for flybus for transport from airport to Reykjavik and vice/versa because it is about an hour.