As others are saying, think carefully. You will NOT have time to see anywhere else in Scotland - but that is not necessarily a bad thing. You would not 'see England' in a few days, so 'seeing Scotland' with all it's islands and remote places is also one for multiple trips. The islands, Orkney included, all have varied character and are all worth a trip of their own. As someone who does not sound like they have seen much (if any) Scotland before, and island is a unique and amazing experience. You are closer to Norway than London, and it feels it...
The Orkney islands are loaded with history and huge amounts of nature. You cannot help but see nature there.
Orkney does have good public transport by island standards. But London Transport it is not! That said, you can plan around it much more than the other islands in my experience, and all are better than many rural parts of mainland Scotland.
A flight up would work - there is then a bus into Kirkwall from the airport (usually timed with the flights).
Base yourself in Kirkwall. Lots of accommodation and more to do if the weather does not play ball.
You can get the bus to Skara Brae or pay for some of the tours e.g. https://www.see-orkney.co.uk/orkney-tours or sort the service bus - e.g. https://www.google.com/maps/dir/Kirkwall/Skara+Brae+Prehistoric+Village,+Sandwick,+Stromness+KW16+3LR/@59.0632169,-3.3166477,11z/data=!3m1!4b1!4m14!4m13!1m5!1m1!1s0x489afe1e29bc041b:0xf22367934f69e8e8!2m2!1d-2.9622491!2d58.984674!1m5!1m1!1s0x489af7c3cd9c4721:0xca626d855ab94ded!2m2!1d-3.3417332!2d59.0488031!3e3?entry=ttu&g_ep=EgoyMDI1MDMxMi4wIKXMDSoASAFQAw%3D%3D
From Kirkwall you then have some easy days out to the nearby islands. Most of the ferries leave from Kirkwall itself. There are cracking days out to Eday, Sanday, Westray(s) and Shapinsay. They are all small to walk around or cycle around (with bike hire) and have some basic facilities. You could go with the weather as the ferries are like buses as a foot passenger - turn up and go, run by the council. Each island feels different.
https://www.orkneyferries.co.uk/
In Kirkwall there are a few things to see, or again the service bus would take you to some interesting places for a walk or wildlife spotting.