You can fly to Orkney from Edinburgh as well. It's a connection through Inverness. When we did it we didn't change planes in Inverness. This is the fastest way to get there. It's easy to spend a lot of time on Orkney. The Mainland does have a lot of places to see and visit, with RIng of Brogdar, Scarra Brae, Stones of Stenness, Maeshowe, Ness of Brogdar and more. But there if more to the place that the neolithic sites. If you are a whisky fan, Highland Park is one of the best single malts out of Scotland and is located just outside of Kirkwall. Also, on the island are jewelry designers and other artists whose studios are interesting to visit. Then drive over the Churchill Barriers to South Ronaldsay. The Italian Chapel is well worth a visit. St. Margaret's Hope is lovely little village for lunch and way down at the souther tip is the Eagles Tomb. An easy trip on a ferry leaving from Kirkwall is to Shapinsay where you can see Balfour Castle. There is a lovely walled garden. For the more adventurous the Isle of Hoy is more rugged and has some nice walks.
Here are some very useful websites. Orkneyjar also includes information on the Ness of Brogdar. The VisitOrkney site lists tour companies. Here's one if you end up wanting to move there. And here's the one from Undiscovered Scotland. HEre's the great National Geographic article.
There are some marvelous videos. Here's one on the Ness of Brogdar. Just check Youtube for many more.