Prestwick airport is the only airport in Scotland that has a direct rail connection between Ayr and Glasgow Central, usually a half hourly service. .You can get half priced rail tickets, upon production of your flight confirmation/boarding pass from/to anywhere in Scotland to/from Prestwick.
At Edinburgh - the tram (£5.50 one way) will take you to Edinburgh Gateway station (for trains to Fife stations, Perth, Dundee and onwards to Inverness and Aberdeen. The tram will also take you to the city centre, via Edinburgh Park station, for trains to Stirling, Dunblane, Glasgow, Airdrie etc You can also get the 747 bus to Inverkeithing station in Fife to then get trains (bus to platform here is about 30 metres away) to Perth, Dundee, Aberdeen and Inverness. There are direct buses from the airport to Glasgow Buchanan Street bus station, to Bathgate, and 24/7 to Edinburgh city centre. If you have a Freedom of Scotland pass, this is valid on the tram.
Glasgow's airport is about 2 miles from Paisley Gilmour Street station From there you can get a train to the city centre. There is also a regular bus service direct to Glasgow Central/Queen street station. You can buy combined train/bus tickets from anywhere in Scotland to Glasgow International airport.
Aberdeen airport, as the crow flies, is near Dyce station, however the passenger terminal is quite a distance to the station, and is a 30 minute bus ride that does not take a direct route, and only operates a limited day time service weekdays. This may still be beneficial if you are taking a train towards Elgin and Inverness. There is however a regular bus service to the city centre bus station, which is adjacent to Aberdeen train station.
There is no train station at Inverness airport - a limited bus service operates to the city centre, and also to Nairn. It is a 15 minute taxi ride to Nairn station if heading East by train towards Aberdeen.
Aberdeen ferry terminal (for the Shetlands and Orkney) is a 10 minute walk from the train station. At Thurso, there is usually a shuttle bus from the train to the ferry to Orkney. At Mallaig - it is a 5 minute walk to where the ferries depart. At Oban, the ferry terminal is adjacent to the train station. You can take a train from Edinburgh to Newcastle (90 minutes) to take the nightly DFDS ferry to IJmuiden, for Amsterdam. The STENA ferry to Belfast leaves from Cairnryan, and offers a shuttle bus from Ayr station to connect to their 3 daily services. (Combined discount train/bus/ferry tickets from £33 one way from most central Scotland stations). Cal Mac ferries depart from adjacent to train stations at Gourock, Ardrossan Harbour, Weymss Bay, and Largs.
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