One-day hiking trip from Edinburgh

As a golfer, I'd say go to St Andrews, which is an easy train ride to Leuchars, then a quick local bus.
I find the area even more beautiful than on TV. However, good weather makes the day much more pleasant. Safe travels!

The Borders and Hadrian's Wall as a one day combo is best done as a Rabbies tour.

The Borders you could do easily by train from Edinburgh to Galashiels, then Borders Buses local bus services, depending on exactly what you wanted to do in the Borders.

Hadrian's Wall would usually be an easy day trip by train via Newcastle (a bit over 2 hours each way) then the AD122 bus. However the local bus company have an indefinite strike starting on 28 October. I can give you no promises on what, if any bus service will be operated in that period, or how long the strike will last.

You could do Glencoe, but it is a long bus ride changing at Glasgow, and bear in mind the short hours of daylight, it is very questionably worth it- you will likely only get a 3 to 4 hour walk in, and be very late back- not the best idea before an early flight next day.

If you give us some idea about where in the Pentland Hills you want to walk we can give you more specific advice.

St Andrews on the train or the bus would be the easiest- there is a direct bus every hour, and an indirect one every hour which runs through the coastal villages of the East Neuk.

I'd advise against hiking in Glencoe in November, especially solo. You need to have the gear and a plan if you're out where there's serious hills in Scotland that time of year. You'd need to be wary of how high you were getting on the hills, just in case you get caught out by weather.

Pentland Hills is much more do-able to get some time outdoors. I'd maybe be looking to get to Penicuik and then to Flotterstone for the Pentland Hills Regional Park. Other contributors may be able to suggest the best way to do that by public transport.

Well, if you want Flotterstone you need Houstons 101/102 service to Biggar (certain journeys extend all the way to Dumfries, an epic and very scenic bus journey).

Scotland has many great bus journeys, but the southern section especially, from Abington motorway services to Dumfries is one of the best IMO, and is an almost unknown route to non-locals. I have been the only person on before now- when it was run by Stagecoach.

I'm used to driving everywhere in Scotland so my knowledge of transport is lacking. Thank you. That does sound like a great day out on an epic bus ride.

Peebles was mentioned before. There should be some fairly flat walking (walking = hiking in British English, more or less) along the River Tweed from Peebles. Others may help route plan.

The East Neuk of Fife was mentioned earlier. Destinations might include Pittenweem or Anstruther. The Fife Coastal Path is set up for what would be some great day hiking.

You may find these two Steve Marsh videos about the Fife Coastal Path useful-
https://www.youtube.com/watch?v=O5e8Ck0EZaY
https://www.youtube.com/watch?v=cN9rXqjzFx4

This is one possible walk from Peebles- https://scotlandstartshere.com/tours/tweed-valley-railway-path/

Use the X62 hourly from Edinburgh (which extends to Galashiels), or you could take the infrequent 91 to Biggar, then the aforementioned 101/102 back to Edinburgh.
Or from Galashiels take the X95 to Hawick (on the way back that goes all the way to Edinburgh on a different route).

Get a 'Borderless 24 hour' ticket on the Borders buses app for £10.15 for all Borders buses that day (as far as Berwick on Tweed and Carlisle)

https://www.wikiloc.com/hiking-trails/flotterstone-balerno-37858376
this is a walk I have done many times , though not for a few years, you can get a bus to Flotterstone and walk through to Balerno and bus back into the city from there, or the other way round

Looks like a good walk at 7.5 miles. Looks quite high at its highest point too. Some good views I'd imagine.

[edit: to remove dull anecdote]