Here are some YouTube videos/channels that might be a good place to start --
This channel is from Wolter's World. A college professor who is making travel videos.
Wolter's See & Do Reykjavík
5 Things You Will Love & Hate Reykjavík Iceland
Top 10 Iceland
Tipping in Iceland
10 Shocks of Iceland
Channel Iceland With a View. American Expat in Iceland making videos on Iceland travel.
The prevailing advice is often the suggestion to make a Ring Road tour of Iceland or to book multi-day tours of other regions. So you might want to look into the possibilities of such tours. Personally, my trip to Iceland was 10 nights and I stayed in in Reykjavík the whole time while booking and enjoying day tours from the city.
I did three day tours with GeoIceland covering the Golden Circle, Snæfellsness Peninsula, and the South Coast. One reason I used them was because they offered small group tours as I did not want to stuck on crowded coaches and tours. https://geoiceland.com/
I also used Arctic Adventures for a lava tube carving tour and a whitewater rafting trip -- https://adventures.is/
These are certainly not the only tour companies, just the ones that I booked with.
Another company offering a lava cave tour -- https://insidethevolcano.com/
Hope this is a helpful start.