Day trip from Glasgow or Edinburgh

Oban is a very long way from Glasgow or Edinburgh- 3 hours each way from Glasgow, 4 hours from Edinburgh.
Likewise Inverness (for Culloden) is getting on for 4 hours.
Much closer would be the Falkirk Wheel, St Andrew's, Dundee, the Scottish Seabird centre at North Berwick etc.
There are boat trips to the islands in the Forth Estuary.
Yes Water of Dean is walkable from Central Edinburgh. Leith, for the Royal Yacht is walkable, has lots of buses and by September will have the extended tram route.
From Glasgow there are lots of easy day trip possibilities without going to Oban.
There are never trains to Edinburgh Airport- it is trams or airlink bus. Leaving early on Sunday it would be the airlink bus.

From Edinburgh consider Stirling, or the East Lothian castles, or a bus to Roslin Chapel

From Glasgow, how about Loch Lomond? Or take a train to Some of the seaside towns south of Glasgow like Weymess Bay, Or Largs. If you are a golfer, Troon might be a, good stop. Or check out some of the Calmac ferriy routes to The Isles of Arran or Bute, which would need a train to get to the ferry departure point. Or train to Gourock and ferry across to Dunoon, a Victorian era seaside town. Nice stroll along the waterfront with views over the Firth of Clyde, Holy Loch and Loch Long.

I took a day trip from Glasgow to Stirling and loved it. It was an easy 30 minute trip from the Queen St. train station. It was one of my favorite places I went to.

Lanlubber, I forgot about Arran! You can get there by train from Glasgow and then catch the approximate 50 minute ferry from Ardrossan to Arran. https://www.calmac.co.uk/ports/ardrossan

Arran was absolutely beautiful and I loved my 3 night stay there, but it could easily be done as a day trip. I think that a lot of Glaswegians do that, and I met a few day trippers there. The ferry takes you to the main town of Brodick, which has some charming places there. You could go on some hikes or visit the castle, which is just north of Brodick. There are some fun shops there, too, like Arran Aromatics and Arran Cheese Shop.

From Largs you can cross on CalMac to the 3 mile long Isle of Great Cumbrae- a lovely place to walk (or cycle) around.

From Dunoon it is possible to catch transit to Colintraive for a ferry across to the Isle of Bute, then the ferry back to Wemyss Bay- a great circular trip.
There is also a local bus from Dunoon to Inveraray (for the Castle), then Citylink inter city coach back to Glasgow- another superb circular trip.
There is also the wonderful Benmore Botanic Gardens just outside Dunoon- there are a couple of local bus routes which will get you there as it's not really walking distance of the ferry.
Dunoon also has two Museums.

About 7 miles south of Edinburgh is Rosslyn Chapel (of Da Vinci Code fame). It's a pretty little spot in its own right - with hiking trails thru the woods to an old castle aside from a tour of the chapel itself. A short walk away is the little village of Roslin which has a couple of cute little tea rooms.
There's bus service from the city to Roslin or, alternatively, the Chapel is close enough to make a taxi or Uber ride out there and back a viable option, as described on the website.

If you check the Rosslyn website there are instructions for getting there by bus - you don't need your own car, taxi or uber...And it will be a lot cheaper too!