Was there in November for Airwaves. Three days definitely enough for the city. Make sure to download Reykjavik Grapevine’s “Appy Hour” app to keep track of what bars are doing deals.
We stayed next to Hlemmur Square, there’s a nice food hall there with traditional and modern options. Get a hot dog from Baejarins Betsu Pyslur.
I really enjoyed the Perlan museum, I’m a real geography nerd so it was perfect for me. The hill it’s on has some nice short walking trails too - we walked down to the Geothermal beach from there, weren’t brave enough to take a dip though!
My one regret from the trip was not taking more time to just go to hot springs and chill. We did the Secret Lagoon as part of the Golden Circle tour and it was gorgeous, a nice cheaper alternative to Blue Lagoon. There’s plenty of municipal facilities for it in Reykjavik itself too.
We did a south coast tour too taking in Skogafoss and Reynisfjara black sands beach which was great. Don’t bother going to the DC-10 plane wreck though.
Weather was bearable for me there in November but I run hot. I imagine January would be worse, depends on prevailing winds I guess