The train
ScotRail runs from Edinburgh Waverley to Glasgow Queen Street in about fifty minutes, with several departures an hour through the day. It is one of the easiest city pairs in Britain. You do not need to treat it as a precious Advance ticket unless you are travelling at the exact peak or with a bike and a plan. You do need to notice the station name in Glasgow.
Queen Street is not Central
Queen Street is the Edinburgh arrival, a few minutes' walk from Buchanan Street, George Square and the Merchant City. Glasgow Central is the grand station for trains to England, including London Euston services, and it sits a short walk south of Queen Street. They are close enough to walk between with a light bag and far enough to annoy you in the rain with a heavy one. If your onward ticket says Central and your Edinburgh train says Queen Street, leave ten minutes to cross, not two.
In Edinburgh, Waverley is the start. Haymarket is worth boarding at if your hotel is in the West End and the train stops there — many of these Glasgow services do.
The other options
The M8 is about an hour to an hour and a quarter when it moves, and a car park problem at both ends when it does not. The coach is the cheaper seat and the slower one. Flying between Edinburgh and Glasgow is not a plan. If the wider trip needs a car for the Highlands, pick it up in Glasgow or Edinburgh on the morning you leave the cities, not for this hop.
How to split the days
Edinburgh takes the castle, the Mile and a viewpoint. Glasgow takes Kelvingrove, the West End and a long dinner. Two nights in Edinburgh and one in Glasgow is the usual shape. The reverse works if you care more about museums and music than about the castle. Inverness is a different journey again — the Highland line, most of three hours — and belongs in the Inverness guide, not in this afternoon.
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