I agree that Undiscovered Scotland is a great resource. Have you looked into the bus schedules? I would recommend reaching to the local VisitScotland Center for help. Here's a link to the one for Stirling. I googled Visitscotland Stirling visitor center which got me off the national site and to local information.
I usually have a car when I go to Scotland as there are a lot of places that are hard to reach by train. I know some people have used buses successfully, but use has been limited. Let's start with Orkney which has decent advice here. But rather than trying to go by local bus, you might want to go on some day tours. Here's the link for Orkney. In terms of place there are so many! If you can get over to Hoy, the Longhope Lifeboat museum and memorial is good. There was a terrible tragedy 50 years ago when the lifeboat went out into the Peatland firth and didn't survive. Here's a BBC article on the 50th anniversary. The Tomb of the Eagle on South Ronaldsay is interesting too. You walk out to the cliffs and then into the tomb. It's all very local. You should look for music while you are there. If you are lucky there will be sessions or gigs. Fiona Driver and the Wrigley Sisters are local. Also, It's any easy ride across on the ferry to Shapinsay where you can see the Balfour Castle. There is lovely walled garden with apple trees.. Also, one of the wonderful things about Orkney is the crafts. See the Orkney Creative Trail. Save money to buy jewelry and or sweaters. They do the best ones in Scotland in my view. :) And if you are a whisky drinker, Highland Park is hard to beat.
In Inverness, you can also check on day tours. There are usually a lot of them. There are some lovely walks in the area. If you want to walk along the Moray Firth go to Culbin Sands. I would recommend a visit to Fort George for the views alone. But it is also interesting from a historical perspective. England's response to the Highland uprisings. The visitor center at both Culloden and Urquhart Castle is good.
On Skye, the boat trip from Elgol gives you great views of Loch Coruisk and the Cuillins. There is a great jewelry store, Skye Silver. There is also a broch, Dun Beag, which is well worth checking out. The view of Niest Point Lighthouse is amazing.
Between Portree and Glencoe are some interesting places. Just outside of Fort William is Glenfinnan of Harry Potter Viaduct fame, but this is also where Prince Charlie first landed when he came to Scotland for the '45 uprising. You would have to head a bit east from Fort William to see the Commando Memorial near Spean Bridge. The commandos of WWII trained in the area. So even if you don't see the memorial think of them as you go through Fort William.
Glencoe is beautiful. Try to find ways to stop and just enjoy the views of the Glen.
For Stirling, I still think it is worth seeing Bannockburn. Don't miss the Argyll's lodging down the hill from the castle. The George Wallace monument offers good and different views than the castle. Mind unless it's changed there isn't a guard rail at the top!
In Edinburg I love the castle. I also enjoy Dynamic Earth. That's the geologist in me. I love getting the Scottish perspective (examples) on things I've only viewed through a North American lens. If you don't want to climb Arthur's seat an alternative is Calton Hill.
You should consider the Trossachs. Just ran out of room.
